Let
\[
S=\left\{\theta \in\left(0, \frac{\pi}{2}\right) ; \sum_{m=1}^{9} \sec \left(\theta+(m-1)...
Let
\[
S=\left\{\theta \in\left(0, \frac{\pi}{2}\right) ; \sum_{m=1}^{9} \sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\right\}
\]
Then
(a) \( S=\left\{\frac{\pi}{12}\right\} \)
(b) \( S=\left\{\frac{2 \pi}{3}\right\} \)
(c) \( \sum_{\theta \in S} \theta=\frac{\pi}{2} \)
(d) \( \sum_{\theta \in S} \theta=\frac{3 \pi}{4} \)
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