Mock AIME 2 2006-2007 Problems/Problem 8

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Problem

A regular polygon of $\displaystyle 2007$ sides is inscribed in a circle. If three distinct vertices of the polygon are selected at random, the probability that the center of the circle lies in the interior of the triangle is $\displaystyle \frac ab.$ Given that $\displaystyle a$ and $\displaystyle b$ are relatively prime positive integers, find $\displaystyle ab.$

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