Complicated Complex Fractions

Algebra Level 5

Let x,yx, y and zz be complex numbers such that

x+y+z=2x + y + z = 2

x2+y2+z2=3x^2 + y^2 + z^2 = 3

xyz=4xyz = 4.

Evaluate

1xy+z1+1yz+x1+1zx+y1|\frac {1}{xy + z - 1} + \frac {1}{yz + x - 1} + \frac {1}{zx + y - 1}|

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