Triangle A B C has \angle C=60^{\circ} and B C=4. Point D is the midpoint of \overline{B C}. What is the largest possible value of \tan (\angle B A D) ?
Answer Choices
A. \dfrac{\sqrt{3}}{6}
B. \dfrac{\sqrt{3}}{3}
C. \dfrac{\sqrt{3}}{2 \sqrt{2}}
D. \dfrac{\sqrt{3}}{4 \sqrt{2}-3}
E. 1