1. The problem is to find the exact value of $\sin \frac{2\pi}{3}$. 2. Recall that $\sin(\theta)$ for angles in radians can be found using the unit circle or sine addition formulas. 3. Note that $\frac{2\pi}{3}$ radians is in the second quadrant where sine values are positive. 4. Use the identity $\sin(\pi - x) = \sin x$. 5. Here, $\frac{2\pi}{3} = \pi - \frac{\pi}{3}$, so $\sin \frac{2\pi}{3} = \sin \left(\pi - \frac{\pi}{3}\right) = \sin \frac{\pi}{3}$. 6. The exact value of $\sin \frac{\pi}{3}$ is $\frac{\sqrt{3}}{2}$. 7. Therefore, the exact value of $\sin \frac{2\pi}{3}$ is $\frac{\sqrt{3}}{2}$.