The possible values of \( \theta \in(0, \pi) \) such that \( \sin (...

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The possible values of \( \theta \in(0, \pi) \) such that \( \sin (\theta)+\sin (4 \theta)+\sin (7 \theta)=0 \) are
[2011 AIEEE]
\( \mathrm{P} \)
(a) \( \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
(b) \( \frac{\pi}{4}, \frac{5 \pi}{12}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
\( \mathrm{W} \)
(c) \( \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{35 \pi}{36} \)
(d) \( \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
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