Answer
$38.491580^{\circ}$
Work Step by Step
Use the identity $\tan\theta=\frac{1}{\cot\theta}$. If $\cot\theta=1.2575516$, then
$\tan\theta=\frac{1}{1.2575516}$
We can find $\theta$ now by using degree mode and the inverse tangent function.
$\theta=\tan^{-1} (\frac{1}{1.2575516})\approx 38.491580^{\circ}$
