Complicated Complex Fractions

Algebra Level 5

Let $x, y$ and $z$ be complex numbers such that

$x + y + z = 2$

$x^2 + y^2 + z^2 = 3$

$xyz = 4$ .

Evaluate

$|\frac {1}{xy + z - 1} + \frac {1}{yz + x - 1} + \frac {1}{zx + y - 1}|$