Cos^2x+cos^2*2x+cos^2*3x+cos^2*4x=2

(1+cos2x) / 2 + (1+cos4x) / 2 + (1+cos6x) / 2 + (1+cos8x) / 2=4

4+cos2x+cos4x+cos6x+cos8x=4

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

2cos5xcos3x+2cos5xcosx=0

2cos5x (cos3x+cosx) = 0

2cos5x*2cos2xcosx=0

cos5x=0⇒5x=π/2+πn⇒x=π/10+πn/5

cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2

cosx==0⇒x=π/2+πn