I am conceptually confused about the dimensions of the angular directions in a metric tensor.
For instance, consider \begin{equation} ds^2 = \frac{1}{x^2}(-dt^2 + dr^2 + r^2 d \theta^2) \end{equation} I never see the angular components, here $d\theta^2$, not accompanied by a length squared term. The RHS, $ds^2$, is length squared. Same goes for $dr^2$ and $dt^2$ (in natural units of course). But $r^2 d \theta^2$ should to me be length squared and angle squared? Are the angular directions dimensionless? I am confused...
