# Trigonometric Arithmetic I

**Geometry**Level 3

\(\begin{cases} x+y=\tan^{-1}{ \frac { 2a }{1-a^2} }\\ \tan{x}\tan{y}=a^2,\end{cases}\) \( \left| a \right| <1\)

\((x-\tan^{-1}{a})^{2015}+(y-\tan^{-1}{a})^{2015}=?\)

\((x-\tan^{-1}{a})^{2015}+(y-\tan^{-1}{a})^{2015}=?\)

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