Cosines And Pies

Geometry Level 4

cosπ15cos2π15cos3π15cos4π15cos5π15cos6π15cos7π15=2n\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 nn satisfying the equation above.

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