cos²2x = 1+cos4x/2

cos4x = 2cos²2x-1

2- sin2x + 2(1-sin²2x) - 1 = 0 

2 - sin2x + 2 - 2sin²2x - 1 = 0

2sin²2x + sin2x - 3 = 0 

sin2x = a

2a² + a - 3 = 0

a1 = -6/4  не подходит

а2 = 1

sin2x = 1

2x = π/2 + 2πn

x = π/4 + πn