p215 q10
thanks
1. Your answer of $\displaystyle \frac{2n\pi}{3} \pm \frac{\pi}{6}$ is correct, the book's answer of $\displaystyle 2n\pi + \frac{\pi}{6}$ misses solutions $\displaystyle \left( \text{such as} \, \frac{5\pi}{6} \, \text{and} \, \frac{\pi}{2}\right) $ and so is not completely correct .....
2. $\displaystyle \cos^{-1} \left( \frac{-1 + \sqrt{5}}{4} \right) = \frac{2 \pi}{5}$ and $\displaystyle \cos^{-1} \left( \frac{-1 - \sqrt{5}}{4} \right) = \frac{4 \pi}{5}$ are correct exact values. Your corresponding answers are only decimal approximations to these exact answers. But it's a bit tough to expect someone to know these exact values!!!!
It's possible to prove that these are the exact values but it's a bit complicated.