An electric dipole has a fixed dipole moment $\overrightarrow{\mathrm{p}}$which makes angle $\mathrm{\theta }$ with respect to x- axis when subjected to an electric field  $\overrightarrow{{\mathrm{E}}_1}=\mathrm{E}\widehat{\mathrm{i}}$it experiences a torque ${\overrightarrow{\mathrm{T}}}_1=\mathrm{\tau }\widehat{\mathrm{k}}$ when subjected to another electric field ${\overrightarrow{\mathrm{E}}}_2=\sqrt{3}{\mathrm{E}}_1\hat{\mathrm{j}}$ it experiences torque $\overrightarrow{{\mathrm{T}}_2}=-\overrightarrow{{\mathrm{T}}_1}$ The angle $\mathrm{\theta }$ is 

T = PE sin $\mathrm{\theta }$ Torque experienced by the dipole in an electric field , $\overrightarrow{\mathrm{T}}=\overrightarrow{\mathrm{P}}\times \overrightarrow{\mathrm{E}}$
$\overrightarrow{\mathrm{p}}=\mathrm{pcos}\mathrm{\theta }\widehat{\mathrm{i}}+\mathrm{psin}\mathrm{\theta }\widehat{\mathrm{j}};\overrightarrow{{\mathrm{E}}_1}=\mathrm{E}\hat{\mathrm{i}}$

$\overrightarrow{\mathrm{\tau }}=(\mathrm{pcos}\mathrm{\theta }\widehat{\mathrm{i}}+\mathrm{psin}\mathrm{\theta }\widehat{\mathrm{j}})\times \mathrm{E}\left(\widehat{\mathrm{i}}\right)$
$\tau \hat{k}=\mathrm{pEsin}\mathrm{\theta }(-\hat{\mathrm{k}})$....(i)
$\begin{array}{l}{\overrightarrow{\mathrm{E}}}_2=\sqrt{3}{\mathrm{E}}_1\widehat{\mathrm{j}}\\ {\overrightarrow{\mathrm{T}}}_2=(\mathrm{pcos}\mathrm{\theta }\widehat{\mathrm{i}}+\mathrm{psin}\mathrm{\theta }\widehat{\mathrm{j}})\times \sqrt{3}{\mathrm{E}}_1\widehat{\mathrm{j}}\\ \mathrm{\tau }\hat{\mathrm{k}}=\sqrt{3}{\mathrm{pE}}_1\cos \mathrm{\theta }\hat{\mathrm{k}}\dots \dots \text{ (ii) }\end{array}$
From eqns. (i) and (ii)
$\begin{array}{l}\mathrm{pEsin}\theta =\sqrt{3}\mathrm{pEcos}\theta \\ \tan \theta =\sqrt{3}\\ \therefore \theta ={60}^{\circ }\end{array}$