Application Of Derivatives

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 :