Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are $2.8$ (medium –$1$) and $6.8$ (medium – $2$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be ${\tan }^{-1}{\left(1+\frac{10}{\theta }\right)}^{\frac{1}{2}}$, the value of $\theta$ is ______.

(Given for dielectric media, ${\mu }_r=1$)