Find the limit of composition 1

Calculus Level 3

A function is defined as \(f(x)=\sin x\) and \(f \circ f \circ f \circ \cdots \circ f(x)=f_n (x)\), where \(n\) is the number of compositions, for all real \(x\).

Find \(\displaystyle \lim_{n \to \infty} f_n (x) \).

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