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