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