An electric dipole has a fixed dipole moment $\overrightarrow p$, which makes angle $\theta$ with respect to x-axis. When subjected to an electric field $\mathop {{E_1}}\limits^ \to = E\widehat i$, it experiences a torque $\overrightarrow {{T_1}} = \tau \widehat k$. When subjected to another electric field $$\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$$ it experiences a torque $$\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to$$. The angle $\theta$ is: