Missing angle

First, let's create rhombus $AB_{1}CD$ . $\angle BCB_{1} = \angle B_{1}AF=6$ . In $\triangle CFE$ , $\angle CFE = \angle AFE = 60$ . This means that triangles $BAF$ and $B_{1}AF$ are congruent therefore $\angle BAF=6$ . This gives measure of $\angle BAD=(180-108)-2*6=\boxed{60}$ .

Note:

There is a second solution to this problem: 132.