For $0 < \theta < \dfrac{\pi}{2}$, if the eccentricity of the hyperbola $x^2 - y^2 \csc^2\theta = 5$ is $\sqrt{7}$ times the eccentricity of the ellipse $x^2 \csc^2\theta + y^2 = 5,$ then the value of $\theta$ is :