Let's minimise sin!

Geometry Level 5

\[P_n=\prod_{k=0}^{n-1}\left(1-2\sin\left(\frac{2k\pi}{n}\right)\right)\]

Find the minimal value of \(P_n\), where \(n\) is a positive integer.

If you come to the conclusion that no minimum is attained, enter 666 as your answer.

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