Answer
$315^{\circ}$
Work Step by Step
Given-
$\cot\theta$ = - $1$ , $\theta$ belongs to Q IV
We will find reference angle of $\theta$ first using positive value '$1$' and reference angle theorem-
$\cot\theta$ = - $1$ = - $\cot 45^{\circ}$ (As $\cot 45^{\circ}$ = $1$)
Therefore by reference angle theorem, $45^{\circ}$ is the reference angle for desired angle $\theta$
The desired angle $\theta$ is in Q IV,
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $360^{\circ} - 45^{\circ}$
= $315^{\circ}$
