$\overline{a},\overline{b}\&\overline{c}$ are unit vectors such that $|\overline{a}+\overline{b}+3\overline{c}|=4$ Angle between $\overline{a}$ and $\overline{b}$ is ${\theta }_1,$ angle between $\overline{b}$ and $\overline{c}$ is ${\theta }_2$ and angle between $\overline{a}$ and $\overline{c}$ varies $[\frac{\pi }{6},\frac{2\pi }{3}]$ then the maximum value of $\cos {\theta }_1+3\cos {\theta }_2$is