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 $\left| \alpha \right|$ .