\[\tan\frac{\pi}{10}=\sqrt{\frac{5-2\sqrt{5}}{5}}\] \[\tan\frac{\pi}{8}=\sqrt{2}-1\] \[\tan\frac{\pi}{6}=\frac{\sqrt{3}}{3}\] \[\tan\frac{\pi}{5}=\sqrt{5-2\sqrt{5}}\] \[\tan\frac{\pi}{4}=1\] \[\tan\frac{3\pi}{10}=\sqrt{\frac{5+2\sqrt{5}}{5}}\] \[\tan\frac{\pi}{3}=\sqrt{3}\] \[\tan\frac{3\pi}{8}=\sqrt{2}+1\] \[\tan\frac{2\pi}{5}=\sqrt{5+2\sqrt{5}}\]