Let $y=\operatorname{cosec}^{-1}(2)$

$\operatorname{Cosec} y=2$

since,$\operatorname{cosec} \pi / 6=2$

So $\operatorname{cosec} y=\operatorname{cosec} \pi / 6$

Since range is $\operatorname{cosec}^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

Therefore, $\operatorname{Cosec}^{-1}(2)$ is $\Pi / 6$.