Answer
The value of $\tan \frac{4\pi }{3}$ is $\sqrt{3}$.
Work Step by Step
$\frac{4\pi }{3}$ 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,
$\begin{align}
& \tan \frac{4\pi }{3}=\tan \frac{\pi }{3} \\
& \tan \frac{4\pi }{3}=\sqrt{3} \\
\end{align}$
