Adding/subtracting sinusoids I'm trying to calculate resultant function from adding two sinusoids:

$9\sin(\omega t + \tfrac{\pi}{3})$ and $-7\sin(\omega t - \tfrac{3\pi}{8})$

The correct answer is $14.38\sin(\omega t + 1.444)$, but I get $14.38\sin(\omega t + 2.745)$.

My calculations are (first using cosine rule to obtain resultant $v$ as): 
$\sqrt{9^2 + (-7)^2 - (2 \cdot 9 \cdot (-7) \cdot \cos(\pi - \tfrac{\pi}{3} + \tfrac{3\pi}{8}))} = 14.38$

And the angle (using the sine rule):
$\pi - \arcsin(|-7| \sin(\pi - \tfrac{\pi}{3} + \tfrac{3\pi}{8}) / 14.38) = 157$ ° or $2.745$ radians.
The easiest way (to my mind) to solve the problem is to


Use the identity $\sin(A\pm B) = \sin A \cos B \pm \cos A \sin B$, substituting the known numerical values of $\cos B$ and $\sin B$,
Gathering the results to express your sum of sinusoids in the form of $C \sin A + D \cos A$,
Expressing the resulting function as $\sqrt{C^2+D^2} \sin\left(\omega t + \theta\right)$