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Geometry Level 3

Given that \(\tan \theta +\cot \theta =2\). And

\[\Large 2^A = \displaystyle \sum^{2^{2016}}_{n=1}\color{green}{\tan}^{\color{red}{ 2}^{\color{blue}{n}}}\theta+\color{green}{\cot}^{\color{red}{2}^{ \color{blue}{n}}}\theta\]

Compute \(A\).

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