A sequence $\left({a_{n}}\right)_{n\in\mathbb{N}}$ is contractive iff there exists a constant $c$, with $0
$|{a_{n+2}-a_{n+1}}|\leqslant{c}\,|{a_{n+1}-a_{n}}|$, for all $n\in\mathbb{N}$.
Examine if the sequence $a_{n}=({\underbrace{\sin\circ\sin\circ\ldots\circ\sin}_{n-{\rm{times}}}})({n})$, $n\in\mathbb{N}$, is contractive.