\[ \lim_{n \rightarrow \infty, n \text{ multiple of } 47} \sqrt [n] {\sin{\left(\dfrac{\pi}{4n}\right)}\sin{\left(\dfrac{2\pi}{4n}\right)}\ldots\sin\left({\dfrac{(\frac n{47} -1)\pi}{4n}}\right)} = \ ? \]

Note

- A total of \( \frac n{47}-1 \) terms are being multiplied.
- \(n\) is a multiple of 47.

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