Precalculus solving equations

Question

sin(2 theta)+sin(4 theta)=0

Answer 1

sin2θ + sin4θ = 0; sin2θ + 2sin2θcos2θ = 0; sin2θ(1 + 2cos2θ) = 0;

sin2θ = 0; 2θ = nπ; θ = nπ/2; n = 0,±1, ±2, . . .

cos2θ = - 1/2; 2θ = 2π/3 + 2πn or 2θ = 4π/3 + 2πn; θ = π/3 + πn or θ = 2π/3 + πn, n = 0, ±1, ±2, . . .