Hello,
[tex]tg( \frac{a}{2} )=\pm \sqrt{ \dfrac{1-cos(a)}{1+cos(a)} } \\
=\pm \sqrt{ \dfrac{ \dfrac{2}{3} }{ \dfrac{4}{3} } } =\pm \sqrt{ \dfrac{1}{2} } =\pm \dfrac{ \sqrt{2} }{2} \\
+\ if\ \dfrac{a}{2}\ in\ 1\ quadrant\ (or \ 3)}\\
-\ if\ \dfrac{a}{2}\ in\ 2\ quadrant\ (or \ 4)}\\
[/tex]
