Recurring Styles #6 - Trigonometric Recurrence!

Calculus Level 5

\[\Large{ x_{n+1} = \sin(x_n)}\]

Let \(x_0 \in (0, \pi)\) and define the sequence \((x_n)_{n=0}^\infty\) by the recurrence relation given above. Find the value of the following upto 3 places of decimals:

\[\large{\lim_{n \to \infty} x_n \sqrt{n} = \ ? }\]

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