Find the value of $\sin^{-1} \left[ \sin \left( \frac{13\pi}{7} \right) \right]$.

$-\frac{\pi}{7}$

The correct answer is Option (3) → $-\frac{\pi}{7}$ ##

$ \sin^{-1} \left[ \sin \left( \frac{13\pi}{7} \right) \right] = \sin^{-1} \left[ \sin \left( 2\pi - \frac{\pi}{7} \right) \right]$

$= \sin^{-1} \left[ \sin \left( -\frac{\pi}{7} \right) \right] = -\frac{\pi}{7}$