How did they get from 2nd last to last step?
$-\Bigg(\pi - \tan^{-1}\bigg({\frac{1}{\sqrt{3}}}\bigg)\Bigg)=-\frac{5 \pi}{6}$
How did they get from 2nd last to last step?
$-\Bigg(\pi - \tan^{-1}\bigg({\frac{1}{\sqrt{3}}}\bigg)\Bigg)=-\frac{5 \pi}{6}$
There is a mistake: $\frac{\sqrt{5}}{\sqrt{15}} = \frac{1}{\sqrt 3}$. After you fix it, you see that $\tan^{-1}\frac{1}{\sqrt 3} = \frac{\pi}{6}$.