6. In the acute triangle $\triangle A B C$, let the sides opposite to $\angle A, \angle B, \angle C$ be $a, b, c$ respectively. If $\frac{b}{a}+\frac{a}{b}=4 \cos C$, then the minimum value of $\frac{1}{\tan A}+\frac{1}{\tan B}$ is $\qquad$