Verified answer

cos 2θ = 1 - 2sin^2θ

2sin^2θ = 1 - cos2θ

sin^2θ = 1/2 - 1/2 cos2θ = (2 +√3)/(4) = 1/2 + √3/4

- 1/2 cos2θ = √3/4

cos2θ = -√3/2

2θ = 5π/6, 7π/6

θ = 5π/12, 7π//12

because cos 2θ, the period is π

so, answer will be: 5π/12, 17π/12, 7π/12, 19π/12