Answer
$\frac{5\pi }{12}$ is the solution of the given equation.
Work Step by Step
We know that according to the ratio table of trigonometry, the value of $\tan (2*\frac{5\pi }{12})$ is given as $-\frac{\sqrt{3}}{3}$.
$\begin{align}
& \tan 2x=-\frac{\sqrt{3}}{3} \\
& \tan 2.\frac{5\pi }{12}=-\frac{\sqrt{3}}{3} \\
& \tan \frac{5\pi }{6}=-\frac{\sqrt{3}}{3} \\
& -\frac{\sqrt{3}}{3}=-\frac{\sqrt{3}}{3}
\end{align}$
Thus, $\tan 2x=-\frac{\sqrt{3}}{3}$ is true.
