The one where trigonometry dominates $x$ !

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

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

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