Venerable Soul!

Find (x+y)\sum(x+y) if (x,y)(x,y) indicates the pairs that are the solutions of the equation- (x2+1)(y2+1)+2(xy)(1xy)=4(1+xy)(x^{2}+1)(y^2+1)+2(x-y)(1-xy)=4(1+xy)

x,yZx,y \in \mathbb{Z}

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

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