tan((pi/3)*(x-4))=sqrt(3)

$$tan{left (frac{pi}{3} left(x – 4right) right )} = sqrt{3}$$

Дано уравнение
$$tan{left (frac{pi}{3} left(x – 4right) right )} = sqrt{3}$$
преобразуем
$$tan{left (pi left(frac{x}{3} – frac{4}{3}right) right )} – sqrt{3} = 0$$
$$tan{left (pi left(frac{x}{3} – frac{4}{3}right) right )} – sqrt{3} = 0$$
Сделаем замену
$$w = tan{left (pi left(frac{x}{3} – frac{4}{3}right) right )}$$
Раскрываем скобочки в левой части ур-ния

w – sqrt3 = 0

Разделим обе части ур-ния на (w – sqrt(3))/w

w = 0 / ((w – sqrt(3))/w)

Получим ответ: w = sqrt(3)
делаем обратную замену
$$tan{left (pi left(frac{x}{3} – frac{4}{3}right) right )} = w$$
подставляем w:

$$x_{1} = -1$$

x1 = -37.0000000000000

x2 = 32.0000000000000

x3 = 92.0000000000000

x4 = -19.0000000000000

x5 = -79.0000000000000

x6 = -46.0000000000000

x7 = 29.0000000000000

x8 = 80.0000000000000

x9 = 20.0000000000000

x10 = -10.0000000000000

x11 = 2.00000000000000

x12 = -13.0000000000000

x13 = -31.0000000000000

x14 = -82.0000000000000

x15 = -94.0000000000000

x16 = 47.0000000000000

x17 = 53.0000000000000

x18 = 5.00000000000000

x19 = 95.0000000000000

x20 = -40.0000000000000

x21 = 68.0000000000000

x22 = -61.0000000000000

x23 = -67.0000000000000

x24 = -100.000000000000

x25 = -34.0000000000000

x26 = -97.0000000000000

x27 = -43.0000000000000

x28 = 26.0000000000000

x29 = 101.000000000000

x30 = -28.0000000000000

x31 = 89.0000000000000

x32 = 38.0000000000000

x33 = -49.0000000000000

x34 = -88.0000000000000

x35 = 8.00000000000000

x36 = 41.0000000000000

x37 = -16.0000000000000

x38 = -73.0000000000000

x39 = 71.0000000000000

x40 = -22.0000000000000

x41 = 23.0000000000000

x42 = 62.0000000000000

x43 = -4.00000000000000

x44 = -91.0000000000000

x45 = -76.0000000000000

x46 = -7.00000000000000

x47 = 98.0000000000000

x48 = -64.0000000000000

x49 = 74.0000000000000

x50 = -55.0000000000000

x51 = 50.0000000000000

x52 = 83.0000000000000

x53 = 56.0000000000000

x54 = -25.0000000000000

x55 = 14.0000000000000

x56 = 59.0000000000000

x57 = -1.00000000000000

x58 = 77.0000000000000

x59 = 86.0000000000000

x60 = -58.0000000000000

x61 = 35.0000000000000

x62 = -70.0000000000000

x63 = 44.0000000000000

x64 = -52.0000000000000

x65 = 17.0000000000000

x66 = 65.0000000000000

x67 = 11.0000000000000

x68 = -85.0000000000000