If the maximum value of $a$, for which the function $f _ { a } ( x ) = \tan ^ { - 1 } 2 x - 3 a x + 7$ is non-decreasing in $\left[ - \frac { \pi } { 6 } , \frac { \pi } { 6 } \right]$, is $\bar { a }$, then $f _ { \bar { a } } \left( \frac { \pi } { 8 } \right)$ is equal to\\
(1) $8 - \frac { 9 \pi } { 49 + \pi ^ { 2 } }$\\
(2) $8 - \frac { 4 \pi } { 94 + \pi ^ { 2 } }$\\
(3) $8 \frac { 1 + \pi ^ { 2 } } { 9 + \pi ^ { 2 } }$\\
(4) $8 - \frac { \pi } { 4 }$