Решить уравнение sin^2x+sin^2(2x)-sin^2(3x)-sin^2(4x)=0

Sin²x+sin²2x-sin²3x-sin²4x=0
1/2(1-cos2x)+1/2(1-cos4x)-1/2(1-cos6x)-1/2(1-cos8x)=0
1-cos2x+1-cos4x-1+cos6x-1+cos8x=0
(cos8x-cos2x)+9cos6x-cos4x)=0
-2sin3xsin5x-2sin2xsin5x=0
-2sin5x(sin3x+sin2x)=0
-4sin5xsin2,5xcos0,5x=0
sin5x=0⇒5x=π4⇒x=πn/5
sin2,5x=0⇒2,5x=πn⇒x=2π/5
cos0.5x=0⇒0,5x=π/2+πn⇒x=π+2πn
ответ x=πn/5 ,x=π+2πn