$\displaystyle 3(1+\cos\frac{\pi}{9}+\cos\frac{2\pi}{9})\sin120 \pi t +3(\sin\frac{\pi}{9}+\sin\frac{2\pi}{9})\cos120 \pi t$

$\displaystyle = (8.638\cos\frac{\pi}{9})\sin120 \pi t+(8.638\sin\frac{\pi}{9})\cos120 \pi t$

Can anyone give me a hint about how to get from the first line to the second? I know the problem resolves to

$\displaystyle 8.638\sin(120 \pi t + \frac{\pi}{9})$