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.