JEE Math Practice Question

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. A.$$ 8-\frac{9 \pi}{4\left(9+\pi^{2}\right)} $$
2. B.$$8-\frac{4 \pi}{9\left(4+\pi^{2}\right)}$$
3. C.$$8\left(\frac{1+\pi^{2}}{9+\pi^{2}}\right)$$
4. D.$$8-\frac{\pi}{4}$$