Tangent Exponential Formulation

Theorem
For any complex number $z$:
 * $\tan z = i \dfrac {1 - e^{2iz}}{1 + e^{2iz}}$

where $\tan z$ is the tangent and $i^2 = -1$.

Also see

 * Sine Exponential Formulation
 * Cosine Exponential Formulation
 * Arctangent Logarithmic Formulation