Answer
$ \dfrac{\pi}{6}, \dfrac{5\pi}{6}$
Work Step by Step
Since $\csc{\theta}= \dfrac{1}{\sin{\{\theta}}$
As $\csc{\theta} = 2$ , we search figure 22 for points where the y-coordinate $(\sin{\theta}=\dfrac{1}{2})$
The two angles on the unit circle where $\sin{\theta}= \dfrac{1}{2}$ are $\dfrac{\pi}{6}$ and $\dfrac{5\pi}{6}$
$\theta= \dfrac{\pi}{6}, \dfrac{5\pi}{6}$
