Sin^4 (2x) + cos^4 (2x) = 5/8
sin^4 (2x) + 2sin(2x)*cos(2x) + cos^4 (2x) - 2sin(2x)*cos(2x) = 5/8
(sin^2 (2x) + cos^2 (2x))^2 - sin 4x = 5/8
1^2 - sin 4x = 5/8
sin 4x = 1 - 5/8 = 3/8
4x = (-1)^n * arcsin(3/8) + pi*n = (-1)^n * arcsin(3/8) + 180°*n
x = (-1)^n * 1/4*arcsin(3/8) + pi/4*n = (-1)^n * 1/4*arcsin(3/8) + 45°*n
На промежутке [0; 180] находятся корни
x1 = 1/4*arcsin(3/8) ≈ 5,506°
x2 = 1/4*arcsin(3/8) + 45° ≈ 50,506°
x3 = 1/4*arcsin(3/8) + 2*45° ≈ 95,506°
x4 = 1/4*arcsin(3/8) + 3*45° ≈ 140,506°