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A dartboard shaped like a regular octagon has an apothem of 15 inches. The smaller octagon, which is also regular, has an apothem of 8 inches. What is the probability of a randomly thrown dart landing within the shaded region, given that the dart lands inside the larger octagon? Round the answer to the nearest hundredth. (Hint: An apothem is the perpendicular distance from the center of a regular polygon to its side.)
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