Помогите решить уравнение

cos^2 (x) - cos^2 (2x) + cos^2 (3x) - cos^2 (4x) = 0

(1+cos2x) / 2 - (1+cos4x) / 2 + (1+cos6x) / 2 - (1+cos8x) / 2=0

1+cos2x-1-cos4x+1+cos6x-1-cos8x=0

(cos2x-cos8x) + (cos6x-cos4x) = 0

2sin2xsin5x-2sinxsin5x=0

2sin5x (sin2x-sinx) = 0

2sin5x*2sin (x/2) cos (3x/2) = 0

sin5x=0⇒5x=πn⇒x=πn/5

sin (x/2) = 0⇒x/2=πn⇒x=2πn

cos (3x/2) = 0⇒3x/2=π/2+πn⇒x=π/3+2πn/3

Ответ x=πn/5; x=π/3+2πn/3