sin(2*x)+4*cos(x)^(2)=1

$$sin{left (2 x right )} + 4 cos^{2}{left (x right )} = 1$$

$$x_{1} = {atan}{left (frac{Im{left(sqrt{-1 – 2 i} sqrt{2 + i}right)}}{Re{left(sqrt{-1 – 2 i} sqrt{2 + i}right)}} right )} + pi + i left(frac{1}{2} log{left (5 right )} – log{left (sqrt{sqrt[4]{5} sqrt{-1 – 2 i} sin{left (frac{1}{2} {atan}{left (2 right )} right )} + sqrt[4]{5} i sqrt{-1 – 2 i} cos{left (frac{1}{2} {atan}{left (2 right )} right )}} sqrt{- sqrt[4]{5} i sqrt{2 + i} sin{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )} + sqrt[4]{5} sqrt{2 + i} cos{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )}} right )}right)$$

/ / _____________________________________________________________________ ___________________________________________________________________ / / __________ _______
|log(5) | / 4 ___ __________ /atan(2) 4 ___ __________ /atan(2) / 4 ___ _______ /atan(1/2) 4 ___ _______ /atan(1/2) || |im/ -1 – 2*I */ 2 + I /|
x2 = I*|—— – log| / / 5 */ -1 – 2*I *sin|——-| + I*/ 5 */ -1 – 2*I *cos|——-| * / / 5 */ 2 + I *cos|———| – I*/ 5 */ 2 + I *sin|———| || + atan|————————–|
2 / 2 / 2 / / 2 / 2 / // | / __________ _______|
re/ -1 – 2*I */ 2 + I //

$$x_{2} = {atan}{left (frac{Im{left(sqrt{-1 – 2 i} sqrt{2 + i}right)}}{Re{left(sqrt{-1 – 2 i} sqrt{2 + i}right)}} right )} + i left(frac{1}{2} log{left (5 right )} – log{left (sqrt{sqrt[4]{5} sqrt{-1 – 2 i} sin{left (frac{1}{2} {atan}{left (2 right )} right )} + sqrt[4]{5} i sqrt{-1 – 2 i} cos{left (frac{1}{2} {atan}{left (2 right )} right )}} sqrt{- sqrt[4]{5} i sqrt{2 + i} sin{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )} + sqrt[4]{5} sqrt{2 + i} cos{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )}} right )}right)$$

/ / _____________________________________________________________________ ___________________________________________________________________ / / __________ _______
|log(5) | / 4 ___ __________ /atan(2) 4 ___ __________ /atan(2) / 4 ___ _______ /atan(1/2) 4 ___ _______ /atan(1/2) || |im/ -1 + 2*I */ 2 + I /|
x3 = -pi + I*|—— – log| / / 5 */ -1 + 2*I *sin|——-| – I*/ 5 */ -1 + 2*I *cos|——-| * / / 5 */ 2 + I *cos|———| – I*/ 5 */ 2 + I *sin|———| || + atan|————————–|
2 / 2 / 2 / / 2 / 2 / // | / __________ _______|
re/ -1 + 2*I */ 2 + I //

$$x_{3} = – pi + {atan}{left (frac{Im{left(sqrt{-1 + 2 i} sqrt{2 + i}right)}}{Re{left(sqrt{-1 + 2 i} sqrt{2 + i}right)}} right )} + i left(frac{1}{2} log{left (5 right )} – log{left (sqrt{- sqrt[4]{5} i sqrt{-1 + 2 i} cos{left (frac{1}{2} {atan}{left (2 right )} right )} + sqrt[4]{5} sqrt{-1 + 2 i} sin{left (frac{1}{2} {atan}{left (2 right )} right )}} sqrt{- sqrt[4]{5} i sqrt{2 + i} sin{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )} + sqrt[4]{5} sqrt{2 + i} cos{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )}} right )}right)$$

/ / _____________________________________________________________________ ___________________________________________________________________ / / __________ _______
|log(5) | / 4 ___ __________ /atan(2) 4 ___ __________ /atan(2) / 4 ___ _______ /atan(1/2) 4 ___ _______ /atan(1/2) || |im/ -1 + 2*I */ 2 + I /|
x4 = I*|—— – log| / / 5 */ -1 + 2*I *sin|——-| – I*/ 5 */ -1 + 2*I *cos|——-| * / / 5 */ 2 + I *cos|———| – I*/ 5 */ 2 + I *sin|———| || + atan|————————–|
2 / 2 / 2 / / 2 / 2 / // | / __________ _______|
re/ -1 + 2*I */ 2 + I //

$$x_{4} = {atan}{left (frac{Im{left(sqrt{-1 + 2 i} sqrt{2 + i}right)}}{Re{left(sqrt{-1 + 2 i} sqrt{2 + i}right)}} right )} + i left(frac{1}{2} log{left (5 right )} – log{left (sqrt{- sqrt[4]{5} i sqrt{-1 + 2 i} cos{left (frac{1}{2} {atan}{left (2 right )} right )} + sqrt[4]{5} sqrt{-1 + 2 i} sin{left (frac{1}{2} {atan}{left (2 right )} right )}} sqrt{- sqrt[4]{5} i sqrt{2 + i} sin{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )} + sqrt[4]{5} sqrt{2 + i} cos{left (frac{1}{2} {atan}{left (frac{1}{2} right )} right )}} right )}right)$$

x1 = -89.8571411817000

x2 = -83.5739558745000

x3 = 40.0553063333000

x4 = 10.6738237332000

x5 = -33.3084734171000

x6 = -85.6083998103000

x7 = 90.3207887907000

x8 = -69.9004365424000

x9 = -76.1836218496000

x10 = -77.2907705673000

x11 = -38.4845100065000

x12 = -8.17573218837000

x13 = 86.0720474193000

x14 = 62.0464549084000

x15 = -30.1668807635000

x16 = 74.6128255228000

x17 = -63.6172512352000

x18 = 77.7544181763000

x19 = -242.688032490000

x20 = -39.5916587243000

x21 = 18.0641577581000

x22 = 33.7721210261000

x23 = 49.4800842940000

x24 = 57.7977135370000

x25 = -23.8836954563000

x26 = -61.5828072994000

x27 = -60.4756585816000

x28 = -16.4933614313000

x29 = -82.4668071567000

x30 = 71.4712328692000

x31 = -10.2101761242000

x32 = -99.2819191425000

x33 = 13.8154163868000

x34 = -47.9092879672000

x35 = 93.4623814443000

x36 = 54.6561208834000

x37 = -0.785398163397000

x38 = 32.6649723083000

x39 = 64.0808988442000

x40 = -98.1747704247000

x41 = -95.0331777711000

x42 = -54.1924732744000

x43 = 99.7455667515000

x44 = 79.7888621121000

x45 = -74.1491779138000

x46 = 11.7809724510000

x47 = 20.0986016939000

x48 = -3.92699081699000

x49 = 68.3296402156000

x50 = -25.9181393921000

x51 = -19.6349540849000

x52 = -52.1580293386000

x53 = -32.2013246993000

x54 = 5.49778714378000

x55 = -11.3173248420000

x56 = 35.8065649619000

x57 = -96.1403264889000

x58 = 92.3552327265000

x59 = -14.4589174956000

x60 = -55.2996219922000

x61 = 76.6472694586000

x62 = -66.7588438888000

x63 = 4.39063842599000

x64 = 26.3817870011000

x65 = -17.6005101491000

x66 = 42.0897502691000

x67 = 2.35619449019000

x68 = -41.6261026601000

x69 = 55.7632696012000

x70 = 84.0376034835000

x71 = 46.3384916404000

x72 = 24.3473430653000

x73 = 98.6384180337000

x74 = 48.3729355762000

x75 = 96.6039740979000

x76 = 27.4889357189000

x77 = -1449.05961147000

x78 = -67.8659926066000

x79 = -91.8915851175000

x80 = 70.3640841514000

x81 = 168.860605130000

x82 = -1.89254688119000

x83 = -45.8748440314000