An algebra problem by Rahil Sehgal

Algebra Level 4

If \(n \ge 3\) and \(1,\alpha_{1}, \alpha_2, \alpha_3, \cdots \alpha_{n-1}\) are the \(n^\text{th} \) roots of unity, then find the value of

\[\large \underbrace{\sum \sum}_{1\le i<j\le (n-1)} \alpha_i \alpha_j.\]

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