# Summing roots of unity

Algebra Level 5

Let the roots of $x^j=1$ be $\large 1, \omega_{j_{1}} , \omega_{j_{2}} , \dots \omega_{j_{j-1}}$, then find the value of:

$\large \displaystyle \sum_{j=2}^{61} \sum_{i=1}^{j-1} \frac{1}{1 - \omega_{j_{i}}}$

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