it is not clear if the question is asking about the static equilibrium of the pendulum or about its oscillations. In either case we can find the equilibrium angle $\alpha$ of the string to the vertical from a vector diagram.
The accelerations due to gravity (g) and due to the constant electric field (qE/m) add as vectors to give a new effective acceleration due to gravity (g').
The pendulum will hang along the direction of g', or oscillate about the line of g', at equal angles to it left and right. g' is only the bisector of g and qE/m if g=qE/m. Then $\alpha=\frac12 \theta$. So the amplitude of the swing will only coincide with the directions g and qE/m if they are at equal angles from g. This requires g=qE/m.