What is the angle between the directions of electric field at any 1) axial point 2) equatorial point due to an electric dipole ?
I think the question is asking "What is the angle between the directions of Eaxial and Eequatorial due to dipole?"
And the answer is 180o
Remember in the derivations of electric field at these two points.
In axial case E is along dipole moment, and in equatorial case E is opposite to dipole moment. Hence directions of E are antiparallel in the two cases.