Cotangent Exponential Formulation/Proof 2

Proof
We have,, that $z$ is a complex number such that:
 * $\forall k \in \Z: z \ne k \pi$

Therefore:
 * $\sin z \ne 0$

It follows from the definition of the complex cotangent function that:
 * $\cot z$

is well-defined.

Hence: