Pugh Analysis Integral Question

This is Exercise 39 of Chapter 4, Real Mathematical Analysis by Pugh.

Let f : [0, 2π] → R be a continuous function such that$$\int_0^{2 \pi} f(x) \sin (n x) d x=0$$Then show that f is constant.

I know that for all n$$\int_0^{2 \pi}\sin (n x) d x=0$$

but have no idea how to proceed.Thanks in advance.