Find the general solution of the equation $\cos 3 \theta = - \dfrac{1}{\sqrt{2}}$
$\cos 3 \theta = - \dfrac{1}{\sqrt{2}}$
$\implies$ $\cos 3 \theta = \cos \left(\dfrac{3 \pi}{4}\right)$
$\implies$ $3 \theta = 2 n \pi \pm \dfrac{3 \pi}{4} \;\;\; n \in Z$
$\therefore \;$ $\theta = \dfrac{2n \pi}{3} \pm \dfrac{\pi}{4}, \;\;\; n \in Z$