Answer
$18.4^\circ, 135^\circ, 198.4^\circ, 315^\circ$
Work Step by Step
1. Use the identify $csc^2\theta=cot^2\theta+1$, we have $cot^2\theta+1-2cot\theta=4\longrightarrow cot^2\theta-2cot\theta-3=0$ which gives $cot\theta=-1$ and $cot\theta=3$
2. For $cot\theta=-1$ with $\theta\in[0^\circ,360^\circ)$, we can find $\theta=135^\circ, 315^\circ$
3. For $cot\theta=3$ with $\theta\in[0^\circ,360^\circ)$, we can find $\theta=18.4^\circ, 198.4^\circ$
