when does sec^{2}x equal 4?
We could shorten it since the 1st quadrant solution and the 3rd quadrant solutions differ by $\displaystyle \pi$, likewise for the 2nd and 4th quadrant roots, and so we could state:
$\displaystyle x=\frac{\pi}{3}(3k+1),\,\frac{\pi}{3}(3k+2)$ where $\displaystyle k\in\mathbb{Z}$.