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Algebra Level 3

{(x+y+z)(x+y)=30(x+y+z)(y+z)=18(x+y+z)(z+x)=2 \begin{cases} (x+y+z)(x+y)=30\\ (x+y+z)(y+z)=18\\ (x+y+z)(z+x)=2 \end{cases}

Given that x,yx, y and z z satisfy the system of equations above, find the sum of all values of zz.

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