Answer
$\frac{2\pi}{3},\frac{4\pi}{3}$
Work Step by Step
$4sec\theta+6=-2$,
$sec\theta=-2$,
$cos\theta=-\frac{1}{2}$,
$\theta=2k\pi+\frac{2\pi}{3}$ or $2k\pi+\frac{4\pi}{3}$ (k is an integer),
$\theta=\frac{2\pi}{3},\frac{4\pi}{3}$ in $[0,2\pi)$.
