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Geometry Level 5

\[A=\sin\left(\frac{\pi}{55}\right)\sin\left(\frac{2\pi}{55}\right)\sin\left(\frac{3\pi}{55}\right)\cdots\sin\left(\frac{54\pi}{55}\right)\\B=\binom{55}{0}+\binom{55}{1}+\binom{55}{2}+\cdots+\binom{55}{27}\] Find \(2AB\).

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