Let X be the set of all postive real numbers c such that \[\frac{\prod_{k=1}^{n-1} \sin\left( \frac{k \pi}{2n}\right)}{c^n} \] converges as n goes to infinity. Find the infimum of X.

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Let X be the set of all postive real numbers c such that \[\frac{\prod_{k=1}^{n-1} \sin\left( \frac{k \pi}{2n}\right)}{c^n} \] converges as n goes to infinity. Find the infimum of X.