Answer
$$\theta\approx-42.6^\circ$$
Work Step by Step
$$\theta=\cot^{-1}(-1.0886767)$$
Most calculators do not contain inverse function for cotangent, so we need to change it to another function available on the calculator.
$\theta=\cot^{-1}(-1.0886767)$ means that $\cot\theta=-1.0886767$
Now recall and apply the identity: $$\tan\theta=\frac{1}{\cot\theta}=\frac{1}{-1.0886767}\approx-0.9185463$$
Therefore, $$\theta=\tan^{-1}(-0.9185463)$$
Now we can use the calculator to calculate for $\theta$.
However, as the question asks for the value in decimal degrees, do not forget to switch the calculator to the DEG environment.
Using calculator, I get $$\theta\approx-42.6^\circ$$
