E an EasyMethod!

Algebra Level 5

\[\large 1+\dfrac{1}{2-\alpha_1}+\dfrac{1}{2-\alpha_2}+\dfrac{1}{2-\alpha_3}+\cdots +\dfrac{1}{2-\alpha_{n-1}}=~?\]

If \(1,\alpha_1,\alpha_2,\ldots, \alpha_{n-1}\) are \(n^{th}\) roots of unity, find the value of the above expression, taking \(n=9\).

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