Solve for all angles between [0, 360) degrees

Question

-cos² θ = 3-3 sin θ

Answer 1

Given that -cos^2θ = 3 - 3sinθ

                   -(1 - sin^2θ) = 3 - 3sinθ              [ Since sin^2θ + cos^2θ =1 ]

                    -1 + sin^2θ = 3 - 3sinθ

                     sin^2θ + 3sinθ -4 = 0

                     sin^2θ - sinθ + 4sinθ -4 = 0      [ Assume 3sinθ = -sinθ + 4sinθ ]

                     sinθ(sinθ - 1) + 4(sinθ - 1) = 0

                     (sinθ - 1)(sinθ + 4) = 0            

                     (sinθ - 1) = 0 and (sinθ + 4) = 0  

                      sinθ = 1 and sinθ = -4

                       θ = π/2 and θ has no value

Therefore θ = π/2.