Confused about the number of independent components of the curvature tensor

Question

Supposedly the number of independent components of the curvature tensor is $n^2(n^2-1)/12$, where $n$ is the dimension. In the case of $n=2$ this evaluates to $1$, but if I take now for example $$ds^2=R^2d\theta^2 + R^2\sin^2\theta d\phi^2,$$ where $R=const.$ one can show that the curvature tensor has the value $$R^\theta_{\phi\theta\phi}=\sin^2\theta\quad \text{and}\quad R^\phi_{\theta\phi\theta}=1.$$ What exactly am I missing here?