Answer
See the steps.
Work Step by Step
$LHS = \sin{3\theta} = \sin{(2\theta + \theta)} = \sin{2\theta} \cos{\theta} + \cos{2\theta} \sin{\theta}$
$LHS = \sin{2\theta} \cos{\theta} + (1-2 \sin^2{\theta}) \sin{\theta}$
$LHS = 2 \sin{\theta} \cos^2{\theta} + \sin{\theta} - 2 \sin^3{\theta}$
$LHS = 2 \sin{\theta} (1-\sin^2 {\theta})+ \sin{\theta} - 2 \sin^3{\theta}$
$LHS = 2 \sin{\theta} - 2 \sin^3 {\theta} + \sin{\theta} -2 \sin^3 {\theta}$
$LHS = 3 \sin{\theta} - 4 \sin^3{\theta} = RHS$
