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$$\tan4x=\sqrt 3,\qquad 0\leq x \lt \pi$$

4 solutions: $$ \frac{\pi}{12}, \frac{\pi}{3}, \frac{7\pi}{12}, \frac{5\pi}{6}$$

or 3 solutions: $$ \frac{\pi}{12}, \frac{\pi}{3}, \frac{7\pi}{12}$$ (text suggested this and no clues about why $$\frac{5\pi}{6}$$ was excluded

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    It was excluded because books and "official" solutions sometimes have mistakes. And they should have given all the answers with denominator $12$, simplifying hides structure.2012-09-28
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    verifying textbook now, since it is quite credible, i wonder if i made that wrong2012-09-28

2 Answers 2