Solve for $x$: $\tan^{-1}x+2\cot^{-1}x=\large\frac{2\pi}{3}$.

Question

$\begin{array}{1 1}(a)\;-\large\frac{1}{\sqrt 3}&(b)\;\large\frac{1}{\sqrt 3}\\(c)\;-\sqrt 3&(d)\;\sqrt 3\end{array}$