Just a slice, please .....

Consider a rectangle with vertices \((0,0), (7,0), (0,5)\) and \((7,5)\).

Next, of the set of lines that slice this rectangle into two sections, choose a line at random, (uniformly distributed over the angle \(\theta\) the line makes with the positive \(x\)-axis).

The expected value for the area of the smaller of the two sections that the rectangle is divided into by the chosen line can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(a + b\).

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