The curl of a vector field $\vec A$ in spherical coordinates is given by $$\nabla \times \overrightarrow{\mathrm{A}}=\frac{1}{r^{2} \sin \theta} \left| \begin{array}{ccc} \widehat{a}_{\mathrm{r}} & r \widehat{\mathrm{a}}_{\theta} & \operatorname{rsin} \theta \widehat{\mathrm{a}}_{\phi} \\ \frac{\partial}{\partial r} & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial \phi} \\ \mathrm{A}_{\mathrm{r}} & \mathrm{rA}_{\theta} & \mathrm{r} \sin \theta \mathrm{A}_{\phi} \end{array}\right|$$
What is the mathematical reasoning behind the $\frac{1}{r^2sin\theta}$ when finding the curl of a vector in spherical coordinates? How would we derive it?
