Fine exactly all solutions to the given equation

Question

Fine exactly all solutions to the given equation:

2cos^2θ = 3sinθ + 3, 0 ≤ θ ≤ 2pi

Answer 1

2 - 2sin²θ = 3sinθ + 3; 2sin²θ + 3sinθ + 1 = 0; (2sinθ + 1)(sinθ + 1) = 0;

sinθ = - 1; θ = 3π/2;

sinθ = - 1/2; θ = 7π/6 or θ = 11π/6