Use trigonometric identities to solve the trigonometric equation

Question

Use trigonometric identities to solve the trigonometric equation: sin(2θ) +cosθ = 0 exactly for the domain 0 ≤ θ ≤ 2pi

Answer 1

2sinθcosθ + cosθ = 0; cosθ = 0; θ = π/2 or θ = 3π/2;

sinθ = - 1/2; θ = 7π/6 or θ = 11π/6