## Precalculus (10th Edition)

$22.5$ degrees
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: $2\theta=45$ $\theta=22.5$