What is the principal value of $\operatorname{cosec}^{-1}\left(- \sqrt{2}\right)$?

Explanation

1. 01

   Find the angle $\theta$ in the branch $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}$ with $\operatorname{cosec} \theta = - \sqrt{2}$.

2. 02

   That angle is $- \frac{\pi}{4}$.