I'm not sure how general a "sine function" can be, but I'll try this: A*sin(B+C*x).

The first condition implies that C=2.

The second condition implies that sin(B+Pi/3)=0, so B+Pi/3=2*Pi*n for any integer n; I'll try n=0, so B=-Pi/3.

The third condition implies that 0=2A*cos(7Pi/3-Pi/3)=2A*cos(2*Pi)=2A, so A=0.

Therefore, the ONLY possibility is the zero function.

In general, when you have N parameters and N conditions, the parameters are uniquely determined by the conditions.