# Evaluate the integral. {eq}\int_{0}^{2 \pi} \sin^2( \frac{1}{3} \theta) \, \mathrm{d}\theta {/eq}

## Question:

Evaluate the integral.

{eq}\int_{0}^{2 \pi} \sin^2( \frac{1}{3} \theta) \, \mathrm{d}\theta {/eq}

## Half-Angle Identities:

Half-angle identities are trigonometric identities that can be used to express a trigonometric function of a half-angle as a trigonometric function of a single angle. One of the half-angle identities is {eq}\displaystyle \sin\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1-\cos(\theta)}{2}} {/eq}, which gives us:

{eq}\sin^2(\theta) = \displaystyle \frac{1-\cos(2\theta)}{2} {/eq}