I know that $\sin \frac{4 \pi}{3}$ is the same as $\sin (\pi + \frac{\pi}{3})$. I also know that $\sin (\pi + \theta) = -\sin \theta$ for any angle $\theta$. So I can simplify $\sin \frac{4 \pi}{3} = -\sin \frac{\pi}{3}$. Now I need to recall the value of $\sin \frac{\pi}{3}$. I can use the 30-60-90 right triangle, where the hypotenuse is 2, the shorter leg is 1, and the longer leg is $\sqrt{3}$. The angle $\frac{\pi}{3}$ is opposite the longer leg, so $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$. Therefore, $\sin \frac{4 \pi}{3} = -\sin \frac{\pi}{3} = -\frac{\sqrt{3}}{2}$. 
Find $\sin \frac{4 \pi}{3}.$