finding largest value of tan angle

Triangle ABC has angle C = 60 degrees and BC = 4. Point D is the midpoint of BC. What is the largest possible value of tan ( angle BAD ) ?

I have been working on this problem for over a week and I understand it is way over my level, but I can't give up. It's frustrating because the problem seems to be so simple. ( but now i see it looked simple because of my lack of knowledge)

Hoping to get some ideas, I have been studying Trigonometry and Geometry( triangle section only).

So far, I was looking for a way to make DA as small as I can.

Wouldn't that make tan (angle BAD ) the largest?

Or am I hopelessly off?

Vicky.(Headbang)