Isn't symmetry beautiful?

Calculus Level 2

20142014sin(sin(sin(sin(sinx))))2014 timesdx= ?\displaystyle\int_{-2014}^{2014}\underbrace{\sin(\sin(\sin(\ldots\sin(\sin x)\ldots)))}_{\mbox{2014 times}}\, dx = \ ?

Give your answer to 3 decimal places.

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