Question 24Triangle $ABC$ has $\angle C = 60^\circ$ and $BC = 4.$ Point $D$ is the midpoint of $BC.$ What is the largest possible value of $\tan(\angle BAD)?$$\dfrac{\sqrt{3}}{6}$$\dfrac{\sqrt{3}}{3}$$\dfrac{\sqrt{3}}{2\sqrt{2}}$$\dfrac{\sqrt{3}}{4\sqrt{2} - 3}$$1$