Tough Guy in my eyes

Calculus Level 5

\[\displaystyle \int _{ 0 }^{ \frac { \pi }{ 2 } }{ \cos ^{ -1 }{ \left(\dfrac { 1 }{ 1+2\cos { (x) } } \right) } } dx\]

Evaluate the integral. Write the answer to 3 decimals.

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