Is it too what?

Algebra Level pending

\[ \large \begin{cases} (1+x)(1+y)=4y\\ (1+y)(1+z)=4z \\ (1+z)(1+x)=4x \end{cases} \]

Let \(x,y\) and \(z\) be numbers satisfying the equation above, find \(x+y+z\).

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