If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ respectively, then $\frac{M_1}{M_2}=$

$$ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}= $$

In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :