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Let $g:[0, \pi] \rightarrow \mathbb{R}$ be continuous and satisfy

\[

\int_{0}^{\pi} g(x) \sin (n x) d x=0

\]

for all integers $n \geq 2$. Then which of the following can you say about $g?$

- $g$ must be identically zero.
- $g(\pi / 2)=1$.
- $g$ need not be identically zero.
- $g(\pi)=0$.
- None of the above.