If $tan^{-1} x + 2 cot^{-1}x =\frac{2\pi}{3}$, then x =

3 $\sqrt{3}$ $\sqrt{2}$ $\frac{\sqrt{3}-1}{\sqrt{3}+1}$

$\sqrt{3}$

$tan^{-1} x + 2 cot^{-1}x =\frac{2\pi}{3}$ $⇒ tan^{-1}x + 2\left(\frac{\pi}{2}-tan^{-1}x\right)=\frac{2\pi}{3}⇒ tan^{-1}x =\frac{\pi}{3}⇒x = \sqrt{3}$