Is There Any Inverse Trigonometric Identity?

Geometry Level 5

\[\large \displaystyle f(x) = (\arcsin(x))^3 + (\arccos(x))^3 \]

If the sum of the maximum and minimum values of the function \( f \colon \mathbb R \to \mathbb R \) can be expressed as \(\displaystyle \dfrac{a { \pi}^{b}}{c}\), where \(a,b\) and \(c\) are positive integers with \(a,c\) coprime, find \(a+b+c\).

Belated Happy Pi Day!
Based on a 12 Standard Math problem

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