\begin{definition}[Definition:Inverse Cosecant/Complex/Definition 1]
Let $z \in \C_{\ne 0}$ be a non-zero complex number.
The '''inverse cosecant of $z$''' is the multifunction defined as:
:$\csc^{-1} \left({z}\right) := \left\{{w \in \C: \csc \left({w}\right) = z}\right\}$
where $\csc \left({w}\right)$ is the cosecant of $w$.
\end{definition}