Let $\theta$ be an angle such that $\tan \theta = 2.$  Simplify
\[\frac{e^{2i \theta} - 1}{e^{2i \theta} + 1}.\]
Question:
Let $\theta$ be an angle such that $\tan \theta = 2.$  Simplify
\[\frac{e^{2i \theta} - 1}{e^{2i \theta} + 1}.\]
Answer:
Let's think step by step.

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2i
Let $\theta$ be an angle such that $\tan \theta = 2.$  Simplify
\[\frac{e^{2i \theta} - 1}{e^{2i \theta} + 1}.\]
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