if $\alpha$, $\beta$ and $\gamma$ are the roots of equation $x^3-3x^2+3x+7=0$ ($\omega$ is the cube root of unity),then

$\frac{{\alpha}-1}{{\beta}-1}$+$\frac{{\beta}-1}{{\gamma}-1}$+$\frac{{\gamma}-1}{{\alpha}-1}$ is

(a)$\frac{3}{{\omega}}$ (b) ${\omega}^2$ (c) 2${\omega}^2$ (d) 3${\omega}^2$

The question is from the IIT entrance Exam practice material. The Answer marked in the solution booklet is (a) but I am unable to find the way to get it. Please help me out.

Thanks in Advance.


Hint: If $\alpha,\beta,\gamma$ are the roots of $(x-1)^3+8=0$, what are $\alpha-1,\beta-1$ and $\gamma-1$ the roots of?


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