# The one where trigonometry dominates $$x$$!

Calculus Level 5

$\large \displaystyle I = \int_{0}^{\pi/2} \frac{\cos (x) \sin (2x) \sin(3x)}{x} \, dx$

$$I$$ is given as above. Find the value of $$\lfloor 1000I \rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function or greatest integer function.

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