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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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