Dirty Polynomial (200 followers problem)

Algebra Level 5

\(P(x)\) is a polynomial of degree 200. It is know that \(P\left( x \right) =\frac { x-2 }{ { x }^{ 2 }+1 } \) for all integer \(x\) in the domain \(-20<x<20 \).

Find the sum of all coefficients of terms with even degree in the expansion of \(P(x)\).

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