sin(x-pi/3)=0

с изменением знака при 0

Получим:
$$sin{left (x – frac{pi}{3} right )} = 0$$

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$cos{left (x + frac{pi}{6} right )} = 0$$
Это ур-ние преобразуется в
$$x + frac{pi}{6} = pi n + {acos}{left (0 right )}$$
$$x + frac{pi}{6} = pi n – pi + {acos}{left (0 right )}$$
Или
$$x + frac{pi}{6} = pi n + frac{pi}{2}$$
$$x + frac{pi}{6} = pi n – frac{pi}{2}$$
, где n – любое целое число
Перенесём
$$frac{pi}{6}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = pi n + frac{pi}{3}$$
$$x = pi n – frac{2 pi}{3}$$

pi
x1 = —
3

4*pi
x2 = —-
3

x1 = -20.9439510239000

x2 = -14.6607657168000

x3 = -36.6519142919000

x4 = 29.3215314335000

x5 = 98.4365698125000

x6 = 41.8879020479000

x7 = 104.719755120000

x8 = -8.37758040957000

x9 = 48.1710873550000

x10 = -30.3687289847000

x11 = -17.8023583703000

x12 = 10.4719755120000

x13 = -5.23598775598000

x14 = -5644.39480095000

x15 = -86.9173967493000

x16 = -83.7758040957000

x17 = 23.0383461263000

x18 = -61.7846555206000

x19 = -71.2094334814000

x20 = 60.7374579694000

x21 = 76.4454212374000

x22 = -77.4926187885000

x23 = 92.1533845053000

x24 = 13.6135681656000

x25 = -64.9262481742000

x26 = 7.33038285838000

x27 = 35.6047167407000

x28 = 51.3126800086000

x29 = 63.8790506230000

x30 = 57.5958653158000

x31 = 73.3038285838000

x32 = 4.18879020479000

x33 = 67.0206432766000

x34 = 38.7463093943000

x35 = 26.1799387799000

x36 = 54.4542726622000

x37 = -2.09439510239000

x38 = -42.9350995991000

x39 = 79.5870138909000

x40 = -27.2271363311000

x41 = -33.5103216383000

x42 = -52.3598775598000

x43 = -99.4837673637000

x44 = 32.4631240871000

x45 = -96.3421747101000

x46 = -11.5191730632000

x47 = -46.0766922527000

x48 = -49.2182849062000

x49 = 85.8701991981000

x50 = 95.2949771589000

x51 = -24.0855436775000

x52 = -39.7935069455000

x53 = 45.0294947015000

x54 = 16.7551608191000

x55 = -93.2005820565000

x56 = -68.0678408278000

x57 = -90.0589894029000

x58 = -58.6430628670000

x59 = 89.0117918517000

x60 = 70.1622359302000

x61 = 19.8967534727000

x62 = 82.7286065445000

x63 = -80.6342114421000

x64 = -55.5014702134000

x65 = -74.3510261350000

x66 = 1.04719755120000