System of Complex Equations

Algebra Level 3

x,y x, y and zz are complex numbers that satisfy the equations x+y+z=2x+y+z = 2, xy+yz+zx=3xy + yz + zx = 3 and xyz=4xyz =4. Given that 11xyz+11yzx+11zxy=ab \frac {1}{1-x-yz} + \frac {1}{1-y-zx} + \frac {1}{1-z-xy} = \frac {a}{b}, where aa and bb are coprime positive integers, what is the value of a+b a+b?

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