Simplify this fraction with square roots; application to arctangent equation. I need your help.
I don't know how to simplify: $\frac{-1+\sqrt{3}+\sqrt{4+2\sqrt{3}}}{2\sqrt{3}} $
and $\frac{-1+\sqrt{3}-\sqrt{4+2\sqrt{3}}}{2\sqrt{3}}$
Thank you in advance.
I found $1$ and $\frac{-1}{\sqrt{3}}$. Then I have to show that these are solutions of the following equation: $arctan(x)+arctan(x\sqrt{3})= \frac{7\pi}{12}$. How can I do that ?

HINT:
$$4+2\sqrt3=(\sqrt3)^2+1^2+2\cdot1\cdot\sqrt3=(\sqrt3+1)^2$$
