doubt doubt plz help(Trignometry)

\tan 7 \theta=0 \\\ \tan \theta-\binom{7}{3}tan^3 \theta +\binom{7}{5}tan^5 \theta - \binom{7}{7}tan^7 \theta =0 \\ \Rightarrow 7-\binom{7}{3}tan^2 \theta +\binom{7}{5}tan^4 \theta - \tan^6 \theta =0 \\ (\sum{\tan \theta_i})^2=\sum{\tan^2 \theta _i}+2\sum_{i<j}{}{\tan \theta_i.\tan\theta _j}\\ 0=2S-2\binom{7}{5}\ \because \tan^2\theta=\tan^2\(\pi-\theta) \\ \boxed{S=21}