An algebra problem by Soumya Shrivastva

Algebra Level 4

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

\[ \dfrac{\alpha - 1}{\beta - 1} + \dfrac{\beta- 1}{\gamma - 1} + \dfrac{\gamma - 1}{\alpha - 1} .\]

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