Answer
$22.5$ degrees
Work Step by Step
We are given the equation:
$\cot (2\theta)=1,0\lt \theta\lt 90$
$\dfrac{1}{\tan (2\theta)}=1$
$\tan (2\theta)=1$
$0\lt \theta\lt 90$
$0\lt 2\theta\lt 180$
For $0\lt 2\theta\lt 180$, there is only one value of $\theta$ to fit the equation:
$2\theta=45$
$\theta=22.5$
