Tangent Exponential Formulation/Formulation 3

Theorem
Let $z$ be a complex number.

Let $\tan z$ denote the tangent function and $i$ denote the imaginary unit: $i^2 = -1$.

Then:
 * $\tan z = -i \paren {\dfrac {e^{i z} - e^{-i z} } {e^{i z} + e^{-i z} } }$