Find the general value of $\theta$ for the inverse trigonometric function
Solution 1:
$$ \begin{aligned} 9 \sec ^{4} \theta &=16 \\ \sec ^{4} \theta &=\frac{16}{9} \\ \sec \theta &=\pm \frac{2}{\sqrt{3}} \\ \cos \theta &=\pm \frac{\sqrt{3}}{2} \\ \theta &=n \pi \pm \frac{\pi}{6}=\frac{(6 n \pm 1) \pi}{6}, \end{aligned} $$ where $n \in \mathbb{Z}.$