Answer
$\theta=-\frac{\pi}{4}+k\pi$ and $\theta=0.46+k\pi$
Work Step by Step
Use identify $csc^2\theta=1+cot^2\theta$, the equation becomes $1+cot^2\theta=cot\theta+3$ or
$cot^2\theta-cot\theta-2=0$ which gives $cot\theta=-1, 2$. The general solutions for the equation are
$\theta=-\frac{\pi}{4}+k\pi$ and $\theta=0.46+k\pi$ where $k$ is any integer.
