Answer
$\theta = 135^{\circ}$
$\theta = 315^{\circ}$
Work Step by Step
$cot ~\theta = -1$
$\frac{x}{y} = -1$
We can let $x = -1$ and $y = 1$, or we can let $x = 1$ and $y = -1$
Since $x$ and $y$ have the same magnitude, the angle $\alpha$ above or below the x-axis is $45^{\circ}$.
When $x = -1$ and $y = 1$:
$\theta = 180^{\circ} - \alpha$
$\theta = 180^{\circ} - 45^{\circ}$
$\theta = 135^{\circ}$
When $x = 1$ and $y = -1$:
$\theta = 360^{\circ} - \alpha$
$\theta = 360^{\circ} - 45^{\circ}$
$\theta = 315^{\circ}$
