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 $n=9$ .