Solve 8 sin ( 2 θ ) + 2 sin ( θ ) = 0 for all solutions 0 ≤ θ < 2 π

Question

Solve  for all solutions 

Answer 1

4 sin (2θ) + sin θ = 0

4 [2 sin θ cos θ] + sin θ = 0

8 sin θ cos θ + sin θ = 0

sin θ [8 cos θ] = 0

Use Zero Product Rule from Algebra 1 to solve for θ.

The only Trigonometry in this problem is the double angle formula.

Answer 2

Expand the sin 2Φ to get 16 sin Φ cos Φ + 2 sin Φ = 0

sin Φ = 0 and cos Φ = 1/8.