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