When will the holidays come 1

Algebra Level 5

If \(1,\alpha_1,\alpha_2,\alpha_3,\alpha_4\) are fifth roots of unity, and

\[\displaystyle\sum_{i=1}^4 \dfrac{1}{2-\alpha_i}=\dfrac{a}{b}\]

Where \(a\) and \(b\) are coprime integers then find \(a-b\).

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