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$\large\cos\dfrac{\pi}{15}\cos\dfrac{2{\pi}}{15}\cos\dfrac{3{\pi}}{15}\cos\dfrac{4{\pi}}{15}\cos\dfrac{5{\pi}}{15}\cos\dfrac{6{\pi}}{15}\cos\dfrac{7{\pi}}{15}= 2^n$.

Find the value of $n$ satisfying the equation above.

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