Mathematics Q5

Calculus Level pending

Let

$$\large \begin{cases} f ( x) =\sin ( \cos ( \tan x ))) \\ f^n (x) = f^{n-1} (f( x)) \end{cases}$$

If $$\xi =\displaystyle \lim _{ n\to \infty }{ f^{ n }\left( { 2 }^{ \circ} \right)}$$, where $$n$$ is positive integer, find $$\left\lfloor 10^7\xi \right\rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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