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 (-(π)/6, (π)/6), is ā, then f_ā((π)/8) is equal to

If the maximum value of $\displaystyle a$, for which the function $\displaystyle f_a(x)=\tan ^{-1} 2 x-3 a x+7$ is non-decreasing in $\displaystyle \left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$, is $\displaystyle \bar{a}$, then $\displaystyle f_{\bar{a}}\left(\frac{\pi}{8}\right)$ is equal to