Trignometric Horrors I

Geometry Level 3

\(\alpha\) = \(\tan { \frac { 2\pi }{ 7 } } \cdot \tan { \frac { 4\pi }{ 7 } } +\tan { \frac { 4\pi }{ 7 } } \cdot \tan { \frac { 8\pi }{ 7 } } +\tan { \frac { 8\pi }{ 7 } } \cdot \tan { \frac { 2\pi }{ 7 } } \)

Find the absolute value \(\left| \alpha \right| \).