Evaluate: $\;$ $\cos^{-1} \left[\sin \left(\dfrac{\pi}{7}\right)\right]$
$\begin{aligned} \cos^{-1} \left[\sin \left(\dfrac{\pi}{7}\right)\right] & = \cos^{-1} \left[\cos \left(\dfrac{\pi}{2} - \dfrac{\pi}{7}\right)\right] \hspace{1cm} \left[\text{Note: } \cos \left(\dfrac{\pi}{2} - \theta\right) = \sin \theta\right] \\\\ & = \cos^{-1} \left[\cos \left(\dfrac{5 \pi}{14}\right)\right] \\\\ & = \dfrac{5 \pi}{14} \hspace{1cm} \left(\dfrac{5 \pi}{14} \in \left[0, \pi\right]\right) \end{aligned}$