# Oh no!

Calculus Level 5

$\int _{ -\pi }^{ \pi }{ \left( \arcsin { \sin { x } } \right) } \left( \arcsin { \cos { x } } \right) \left( \arccos { \cos { x } } \right) \left( \arccos { \sin { x } } \right) \, dx$

If the integral above can be expressed in the form $$\dfrac { { \pi }^{ \alpha } }{ \beta }$$, where $${ \alpha }$$ and $${ \beta }$$ are positive integers, find $$\dfrac { \beta }{ \alpha }$$.

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