直线 $y=\frac{\sqrt{3}}{3}x+\sqrt{2}$与圆心为D的圆 $\left\{\begin{array}{l}x=\sqrt{3}+\sqrt{3}cos\theta \\ y=1+\sqrt{3}sin\theta \end{array}\right.(\theta \in [0,2\mathrm{\pi }\left)\right)$交与 $A,B$两点，则直线 $AD$与 $BD$的倾斜角之和为(   ).

A．

$\frac{7}{6}\pi$

B．

$\frac{5}{4}\pi$

C．

$\frac{4}{3}\pi$

D．

$\frac{5}{3}\pi$