Answer
See below.
Work Step by Step
Using trigonometric identities, we have:
$LHS=sin(\theta+2\theta)=sin\theta cos(2\theta)+cos\theta sin(2\theta)=sin\theta(1-2sin^2\theta)+cos\theta(2sin\theta cos\theta)=sin\theta-2sin^3\theta+2sin\theta(1-sin^2\theta)=3sin\theta-4sin^3\theta=RHS$