For any integer $k$, let $\alpha _ { k } = \cos \left( \frac { k \pi } { 7 } \right) + i \sin \left( \frac { k \pi } { 7 } \right)$, where $i = \sqrt { - 1 }$. The value of the expression $\frac { \sum _ { k = 1 } ^ { 12 } \left| \alpha _ { k + 1 } - \alpha _ { k } \right| } { \sum _ { k = 1 } ^ { 3 } \left| \alpha _ { 4 k - 1 } - \alpha _ { 4 k - 2 } \right| }$ is