I'm stuck on this radical simplification $$ (\sqrt{5}+1) \sqrt{10+2\sqrt{5}}$$ In my textbook this product is equal to the $tan(\frac{2\pi}{5})$ and the value is : $$ 4 \sqrt{5+2 \sqrt{5}} $$
I tried to do some simplification and I stopped at this step $$ \sqrt{5(10+2\sqrt{5})}+\sqrt{10+2\sqrt{5}}$$