Prove that
`tan alpha+2 tan 2 alpha+2^(2)tan^(2)alpha+..............+2^(n-1)tan2^(n-1)alpha+2^(@)cot2^(@)alpha=cotalpha`

Explanation

To prove the equation:

\[ \tan \alpha + 2 \tan 2\alpha + 2^2 \tan 2^2 \alpha + \ldots + 2^{n-1} \tan 2^{n-1} \alpha + 2^n \cot 2^n \alpha = \cot \alpha \]

we will use the identity:

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