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Find the principal values of the following: <br> $ \mathrm{cosec}^{-1} (-\sqrt 2) $

$\begin{array}{1 1} \large {\frac{-\pi}{4}} \\ \large {\frac{-\pi}{2}} \\ \large {\frac{-\pi}{8}} \\ \large {\frac{-\pi}{6}} \end{array} $

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