Staying in the triangle

Three points are chosen uniformly at random from the boundary of a square and a fourth point is chosen uniformly at random from the interior. The probability that the 4th point lies in the triangle formed by the other 3 points can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b?\)

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