Wolfram is not very helpful here

Since $\left|\dfrac{1}{x^{191}}\right|$ is a decreasing function, we can use the fact that $\tan{x}$ is undefined at every $\dfrac{(2n+1)\pi}{2}, \ n \in \mathbb{Z}$ .

Therefore, $\tan{x}$ is defined $\forall \ x$ such that $|x| < \dfrac{\pi}{2}$ .

Thus, $\left|\dfrac{1}{x^{191}}\right| < \dfrac{\pi}{2} \implies |x^{191}| > \dfrac{2}{\pi} \\ \therefore \dfrac{a}{\pi} = \dfrac{2}{\pi} \implies a = \ \boxed{2}$ .