That's too much of work

Calculus Level 5

\(\displaystyle\int_0^{\pi/4}\)\(\dfrac{\ln(\cot \theta)}{\left((\sin \theta)^{2009}+(\cos \theta)^{2009}\right)^2}\)\((\sin 2\theta)^{2008}\) \(d \theta\) = \(\dfrac{a^b \ln a}{c^a}\)

If the equation above is true, solve the for values of \(a,b,c\) where \(a,b,c\) are in their simplest form. Find the value of \(a+b+c\).

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