## Precalculus (6th Edition) Blitzer

The value of $\tan \frac{4\pi }{3}$ is $\sqrt{3}$.
$\frac{4\pi }{3}$ lies in the third quadrant. So, the reference angle is $\frac{\pi }{3}$. $\tan \frac{4\pi }{3}=\tan \left( \pi +\frac{\pi }{3} \right)$ As $\tan \left( \pi +\frac{\pi }{3} \right)=\tan \frac{\pi }{3}$. So, \begin{align} & \tan \frac{4\pi }{3}=\tan \frac{\pi }{3} \\ & \tan \frac{4\pi }{3}=\sqrt{3} \\ \end{align}