Answer
a) $3$
b)$-9$
Work Step by Step
a) I know that $\cot$ is an odd function, which means $f(-\theta)=-f(\theta).$
Therefore $f(-a)=\cot{(-a)}=-\cot{a}=3$.
b) I know that $\cot$ has a period of $\pi$, hence $\cot{\theta}=\cot{(\theta+k\pi)}$ where $k$ is an integer.
Thus $f(a)+f(a+\pi)+f(a+4\pi)=\cot{(a)}+\cot{(a+\pi)}+\cot{(a+4\pi)}=\cot{(a)}+\cot{(a)}+\cot{(a)}=(-3)+(-3)+(-3)=(-9)$
