Don't always look up to the sky.

All one has to do is realize that point E is a center of a circle going through points A, B, and C. This is obvious from the fact that $\angle AEB=120^\circ$ while $\angle ACB=60^\circ$ .

Then since $AE=EC$ and $\angle AEC=90^\circ$ the $\angle EAC=45^\circ$ and $\angle BAC=45^\circ+30^\circ=\boxed{75^\circ}$