Given that $\triangle A B C$ is an isosceles right triangle with $AB$ as the hypotenuse, $\triangle A B D$ is an equilateral triangle, and the dihedral angle $C - A B - D$ is $150 ^ { \circ }$, then the tangent of the angle between line $C D$ and plane $A B C$ is\\
A. $\frac { 1 } { 5 }$\\
B. $\frac { \sqrt { 2 } } { 5 }$\\
C. $\frac { \sqrt { 3 } } { 5 }$\\
D. $\frac { 2 } { 5 }$