Answer
$y=\dfrac{2\pi}{3}$
Work Step by Step
RECALL:
$y=\text{arcsec}{(x)} \longrightarrow \sec{y}=x$ where $y$ is in the interval $[0, \frac{\pi}{2})\cup (\frac{\pi}{2}, \pi]$.
Note that:
$\sec{(\frac{2\pi}{3})} = -2$
Thus, the solution to the given equation is $y=\dfrac{2\pi}{3}$.
