If the pair of lines ${\mathrm{x}}^2\mathrm{cos\theta }+3\mathrm{xytan\theta }-{\mathrm{y}}^2\mathrm{sin\theta }=0$ are perpendicular to each other then $\mathrm{\theta }$

If the equation ${\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0$represents a pair of perpendicular lines then $\mathrm{a}+\mathrm{b}=0$
For the equation ${\mathrm{x}}^2\mathrm{cos\theta }+3\mathrm{xytan\theta }-{\mathrm{y}}^2\mathrm{sin\theta }=0$
       $\mathrm{a}+\mathrm{b}=\mathrm{cos\theta }-\mathrm{sin\theta }$
Equate to zero, and then find the suitable value for $\mathrm{\theta }$
It implies 
$\begin{array}{c}\mathrm{sin\theta }=\mathrm{cos\theta }\\ \mathrm{tan\theta }=1\\ \mathrm{\theta }=\frac{\mathrm{\pi }}{4}\end{array}$
Therefore, the value of $\mathrm{\theta }$ is $\boxed{\frac{\mathrm{\pi }}{4}}$