Answer
$$cot\theta=\pm\sqrt{csc^{2}\theta-1}$$
Work Step by Step
By identity, $csc^{2}\theta=1+cot^{2}\theta$.
Subtracting 1 from both sides
$csc^{2}{\theta}-1=\cot^{2}{\theta}
\\\cot^{2}{\theta}=\csc^{2}{\theta}-1$
Taking square-root on both sides,
$$\cot\theta=\pm\sqrt{\csc^{2}\theta-1}$$
