Hello. I am stuck on this problem

We are given triangle ABC and point E on segment AC, such that <ABE = 75 deg and <EBC= 75 deg. Also, AB = 4 and BC = 6. Find the areas of triangles ABE and EBC.

Now at first I thought that the angle bisector formed a right angle but now I think it doesn't. By the angle bisector theorem, we can say that $\displaystyle \displaystyle \frac{4}{AE}=\frac{6}{EC}$ but that doesn't get me any further. I can find the area of the triangle by using the law of cosines but that also doesn't help me. I feel like the fact that there is an angle bisector should be a big part of the solution, but I'm stumped.

Any hints?