$$2 \cos (\theta - \frac{\pi}{2}) + 3 \sin (\theta + \frac{\pi}{2}) - (3\sin \theta + 2 \cos \theta)$$ = ?

$$2 \cos (\theta - \frac{\pi}{2}) + 3 \sin (\theta + \frac{\pi}{2}) - (3\sin \theta + 2 \cos \theta)$$ =

$$2 \cos (\theta - \frac{\pi}{2}) + 3 \sin (\theta + \frac{\pi}{2}) - (3\sin \theta + 2 \cos \theta)$$ =

$$cos (\theta - \frac{\pi}{2}) = sin(\theta)$$

$$sin (\theta + \frac{\pi}{2}) = cos (\theta)$$

$$2 \sin(\theta) + 3 \cos(\theta) - (3\sin \theta + 2 \cos \theta)$$ =

$$\cos \theta - \sin \theta$$