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Three sectors are chosen at random from circle \(C,\) having angles \(\frac{\pi}{10}, \frac{2\pi}{10}, \frac{3\pi}{10}\) respectively. The probability that these three sectors have a point in common other than the center of the circle can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b?\)

Details and assumptions

A circle sector is the portion of a disc that is enclosed by two radii and the arc. The angle of the sector is the central angle of the arc.

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