Complex Numbers Simplified?

Algebra Level 5

Let x,y,zx,y,z be complex numbers such that the following equations hold. {x+y+z=   2x2+y2+z2=   3xyz=   4\begin{cases} x+y+z &= ~~~2 \\ x^2+y^2+z^2 &=~~~3 \\ xyz &=~~~4 \end{cases} Find the value of 1xy+z1+1yz+x1+1zx+y1.\dfrac{1}{xy+z-1}+\dfrac{1}{yz+x-1}+\dfrac{1}{zx+y-1}.

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