The  value of $tan^{-1}\sqrt{3}-sec^{-1}(-2)+cosec^{-1}\frac{2}{\sqrt{3}}$, is

$\frac{\pi}{3}$ $\frac{-\pi}{3}$ 0 $\frac{4\pi}{3}$

0

$tan^{-1}\sqrt{3}-sec^{-1}(-2)+cosec^{-1}\frac{2}{\sqrt{3}}=\frac{\pi}{3}-\frac{2\pi}{3}+\frac{\pi}{3}=0$