Regular octagon \(ABCDEFGH\) is inscribed in a circle, as shown below. The sector of the circle bounded by raddi \(\overline{AJ}\) and \(\overline{DJ}\) and by \(\overgroup{AD}\) is shaded. The area of the shaded sector is what fraction of the area of the circle?

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The regular octagon can be divided into 8 equal segments. Only three sides, or segments, are shaded, implying that the shaded region is \(\dfrac{1}{3}\) of the entire circle.