sin(x)^3+cos(x)^3=0

$$sin^{3}{left (x right )} + cos^{3}{left (x right )} = 0$$

-pi
x1 = —-
4

$$x_{1} = – frac{pi}{4}$$

3*pi
x2 = —-
4

$$x_{2} = frac{3 pi}{4}$$

/ / _____________ / / _____________
| | ___ ___ / ___ || | | ___ ___ / ___ ||
| | 1 I*/ 3 / 2 */ 1 – I*/ 3 || | | 1 I*/ 3 / 2 */ 1 – I*/ 3 ||
x3 = 2*re|atan|- – + ——- + ———————-|| + 2*I*im|atan|- – + ——- + ———————-||
2 2 2 // 2 2 2 //

$$x_{3} = 2 Re{left({atan}{left (- frac{1}{2} + frac{sqrt{2}}{2} sqrt{1 – sqrt{3} i} + frac{sqrt{3} i}{2} right )}right)} + 2 i Im{left({atan}{left (- frac{1}{2} + frac{sqrt{2}}{2} sqrt{1 – sqrt{3} i} + frac{sqrt{3} i}{2} right )}right)}$$

/ / _____________ / / _____________
| | ___ ___ / ___ || | | ___ ___ / ___ ||
| |1 I*/ 3 / 2 */ 1 + I*/ 3 || | |1 I*/ 3 / 2 */ 1 + I*/ 3 ||
x4 = – 2*re|atan|- + ——- – ———————-|| – 2*I*im|atan|- + ——- – ———————-||
2 2 2 // 2 2 2 //

$$x_{4} = – 2 Re{left({atan}{left (frac{1}{2} – frac{sqrt{2}}{2} sqrt{1 + sqrt{3} i} + frac{sqrt{3} i}{2} right )}right)} – 2 i Im{left({atan}{left (frac{1}{2} – frac{sqrt{2}}{2} sqrt{1 + sqrt{3} i} + frac{sqrt{3} i}{2} right )}right)}$$

/ / _____________ / / _____________
| | ___ ___ / ___ || | | ___ ___ / ___ ||
| |1 I*/ 3 / 2 */ 1 + I*/ 3 || | |1 I*/ 3 / 2 */ 1 + I*/ 3 ||
x5 = – 2*re|atan|- + ——- + ———————-|| – 2*I*im|atan|- + ——- + ———————-||
2 2 2 // 2 2 2 //

$$x_{5} = – 2 Re{left({atan}{left (frac{1}{2} + frac{sqrt{2}}{2} sqrt{1 + sqrt{3} i} + frac{sqrt{3} i}{2} right )}right)} – 2 i Im{left({atan}{left (frac{1}{2} + frac{sqrt{2}}{2} sqrt{1 + sqrt{3} i} + frac{sqrt{3} i}{2} right )}right)}$$

/ / _____________ / / _____________
| | ___ / ___ ___|| | | ___ / ___ ___||
| |1 / 2 */ 1 – I*/ 3 I*/ 3 || | |1 / 2 */ 1 – I*/ 3 I*/ 3 ||
x6 = – 2*re|atan|- + ———————- – ——-|| – 2*I*im|atan|- + ———————- – ——-||
2 2 2 // 2 2 2 //

$$x_{6} = – 2 Re{left({atan}{left (frac{1}{2} – frac{sqrt{3} i}{2} + frac{sqrt{2}}{2} sqrt{1 – sqrt{3} i} right )}right)} – 2 i Im{left({atan}{left (frac{1}{2} – frac{sqrt{3} i}{2} + frac{sqrt{2}}{2} sqrt{1 – sqrt{3} i} right )}right)}$$

x1 = -85.6083998103000

x2 = 90.3207887907000

x3 = -69.9004365424000

x4 = -38.4845100065000

x5 = 96.6039740979000

x6 = 62.0464549084000

x7 = 74.6128255228000

x8 = -63.6172512352000

x9 = 77.7544181763000

x10 = -76.1836218496000

x11 = 18.0641577581000

x12 = 33.7721210261000

x13 = -3902.64347392000

x14 = 40.0553063333000

x15 = 36.9137136797000

x16 = -13.3517687778000

x17 = -16.4933614313000

x18 = -82.4668071567000

x19 = -47.9092879672000

x20 = 71.4712328692000

x21 = -10.2101761242000

x22 = 80.8960108299000

x23 = 24.3473430653000

x24 = 150.011049209000

x25 = -57.3340659280000

x26 = -98.1747704247000

x27 = -54.1924732744000

x28 = -204.988920647000

x29 = 11.7809724510000

x30 = -3.92699081699000

x31 = 68.3296402156000

x32 = -25.9181393921000

x33 = -19.6349540849000

x34 = -32.2013246993000

x35 = 5.49778714378000

x36 = -79.3252145031000

x37 = 58.9048622548000

x38 = -44.7676953137000

x39 = 1262.13484858000

x40 = 30.6305283725000

x41 = -60.4756585816000

x42 = 99.7455667515000

x43 = 52.6216769476000

x44 = -35.3429173529000

x45 = -41.6261026601000

x46 = 55.7632696012000

x47 = 84.0376034835000

x48 = 46.3384916404000

x49 = 2.35619449019000

x50 = 8.63937979737000

x51 = -91.8915851175000