System of Complex Equations

Algebra Level 3

$x, y$ and $z$ are complex numbers that satisfy the equations $x+y+z = 2$ , $xy + yz + zx = 3$ and $xyz =4$ . Given that $\frac {1}{1-x-yz} + \frac {1}{1-y-zx} + \frac {1}{1-z-xy} = \frac {a}{b}$ , where $a$ and $b$ are coprime positive integers, what is the value of $a+b$ ?