$\text{ Angle between the asymptotes of the hyperbola }{\mathrm{x}}^2+2\mathrm{xy}-3{\mathrm{y}}^2+\mathrm{x}+7\mathrm{y}+7=0\text{ is }$

$$\begin{gathered} Given hyperbola {\mathrm{x}}^2+2\mathrm{xy}-3{\mathrm{y}}^2+\mathrm{x}+7\mathrm{y}+7=0 \\ Since a\mathrm{symptotes} \mathrm{are} \mathrm{parallel} \mathrm{to} {\mathrm{x}}^2+2\mathrm{xy}-3{\mathrm{y}}^2=0 \\ Then a\mathrm{ngle} \mathrm{between} \mathrm{asymptotes} \mathrm{Tan}\mathrm{\theta }=\left(\frac{2\sqrt{{\mathrm{h}}^2-\mathrm{ab}}}{\left|a+b\right|}\right) \\ =\frac{2\sqrt{1+3}}{\left|-2\right|} \\ =2 \\ \Rightarrow \theta ={\tan }^{-1}\left(2\right) \end{gathered}$$