solve the equation on the interval 0≤θ<2π

Question

cos(20) + 6 sin^2 theta =2

Answer 1

cos(2θ) + 6sin²θ = 2

6sin²θ + (1 - 2sin²θ) - 2 = 0

4sin²θ = 1

sin²θ = 1/4

sinθ = 1/2 or -1/2

If sinθ = 1/2, then θ = π/6 or 5π/6

If sinθ = -1/2, then θ = 7π/6 or 11π/6

So, θ = π/6, 5π/6, 7π/6, 11π/6.