Answer
a)$-2$
b)$6$
Work Step by Step
a) I know that $\csc$ is an oddfunction, which means $f(-\theta)=-f(\theta).$
Therefore $f(-a)=\csc{(-a)}=-\csc{a}=-2$.
b) I know that $\csc$ has a period of $2\pi$, hence $\csc{\theta}=\csc{(\theta+2k\pi)}$ where $k$ is an integer.
Thus $f(a)+f(a+2\pi)+f(a+4\pi)=\csc{(a)}+\csc{(a+2\pi)}+\csc{(a+4\pi)}=\csc{(a)}+\csc{(a)}+\csc{(a)}=2+2+2=6$
