If in a triangle \( A B C, \cos 3 A+\cos 3 B+\cos 3 C=1 \), then one angle must be exactly equal...

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If in a triangle \( A B C, \cos 3 A+\cos 3 B+\cos 3 C=1 \), then one angle must be exactly equal to
(a) \( \frac{\pi}{3} \)
(b) \( \frac{2 \pi}{3} \)
(c) \( \pi \)
(d) \( \frac{4 \pi}{3} \)
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