Nested Trigonometric Integral

Calculus Level 3

\[ \large \displaystyle 3\int _{ 0 }^{ 1 }{ \sin { (2\cos ^{ -1 }{ (\sin { (\cos ^{ -1 }{ (x)))) \, dx } } } } } = \ ? \]

Clarification: \( \cos ^{ -1 }{ (x) } =\arccos { (x) } \) is the inverse cosine function.

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