Venerable Soul!

Find \(\sum(x+y)\) if \((x,y)\) indicates the pairs that are the solutions of the equation- \[(x^{2}+1)(y^2+1)+2(x-y)(1-xy)=4(1+xy)\]

\(x,y \in \mathbb{Z}\)

Note-This problem is not mine. \(\sum(x+y)\) indicates sum of all pairs satisfying the equality

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