A calculus problem by Jonathan Schirmer

Calculus Level 4

The following can be expressed as \( \frac{\pi+\ln{a/b}}{c}\) where \(a\) and \(b\) are coprime positive integers:

\[ \int^{\frac{\pi}{4}}_0 \frac{dx}{2+\tan{x}} \]

What is the value of \(a+b+c\)?

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