Separating line

Two points \(P,Q\) are chosen uniformly at random from the interior of the square \(ABCD\). The line \(L_1\) through \(P\) and \(Q\) is drawn. The probability that the points \(A\) and \(C\) are on different sides of \(L_1\) 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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