Evaluate \int_{\frac{\pi}{4}}^{\frac{\pi}{3}} \frac{(\sin ^3 \theta \minus{}\cos ^ 3 \theta \minus{}\cos ^ 2 \theta)(\sin \theta \plus{}\cos \theta \plus{}\cos ^ 2 \theta)^{2007}}{\sin ^ {2009}\theta \cos ^ {2009}\theta}\ d\theta
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