Trigonometry Identities - Sum to Product to Identity (Degrees)

Question

Complete the sum to product identity for this expression

$$	ext{sin}{(120^{\circ})}+	ext{sin}{(330^{\circ})}$$

Accepted Answer

$$=2 	ext{sin}{( \frac{(120^{\circ} + 330^{\circ})}{2})}   	ext{cos}{( \frac{(120^{\circ} - 330^{\circ})}{2})}$$

Answer

$$=	ext{sin}{( \frac{2}{(120^{\circ} + 330^{\circ})})}   	ext{sin}{( \frac{(120^{\circ} - 330^{\circ})}{2})}$$