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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