Notice that two of the intersections of the function with the x-axis are x=-pi/3 and x=2pi/3.
Therefore, in the case of each of the options,
[tex]\begin{gathered} A)-3\cos (2(-\frac{\pi}{3})+\frac{\pi}{3})=-3\cos (-\frac{\pi}{3})\ne0 \\ B)3\cos (2(-\frac{\pi}{3}-\frac{\pi}{3})=3\cos (-\frac{4}{3}\pi)\ne0 \\ C)3\sin (2(-\frac{\pi}{3}+\frac{\pi}{3}))=3\sin (0)=0 \end{gathered}[/tex]Thus, the answer is option C.
