Let's salute cos 2

Geometry Level 4

(1+cosπ10)(1+cos3π10)(1+cos7π10)(1+cos9π10)\left(1+\cos \dfrac{\pi}{10}\right) \left(1+\cos \dfrac{3\pi}{10}\right) \left(1+\cos \dfrac{7\pi}{10}\right) \left(1+\cos \dfrac{9\pi}{10}\right)

Find the reciprocal of the value of the expression above.

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