Question: A segment of a circle is the region enclosed by an arc and its chord. If \(r\) is the radius of the circle and \(\theta\) the angle subtended at the center of the circle, then it can be shown that the area \(A\) of the segment is \(A=\frac{1}{2} r^{2}(\theta-\sin \theta)\), where \(\theta\) is in radians. Find the value of \(\theta\) for which the area of the segment is one-fourth the area of the circle. Give \(\theta\) to the nearest degree.

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