A literal complex system

Algebra Level 3

\[ \large \begin{cases}{x+y+z=2} \\ {x^2+y^2+z^2=3} \\ {xyz = 4 } \end{cases} \]

If \(x,y\) and \(z\) are complex numbers that satsify the system of equations above, find the value of \( \frac1{xy+z-1} +\frac1{yz+x-1}+\frac1{zx+y-1} \).

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