Infinite trigonometric limit

Calculus Level 4

\[\large \lim_{n \to \infty} \cos \left(\frac x2 \right) \cos \left(\frac x4 \right) \cos \left(\frac x8 \right) \cdots \cos \left(\frac x{2^n} \right)\]

Find the above limit at \(x=\dfrac \pi 6\)

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