homework and exercises - Riemann tensors in 3 dimensions

So in 3 dimensions, Riemann tensor has 6 independent terms. So we can fully describe it in terms of the Ricci tensor.

How do I show that $R_{abcd}=T_{ac}g_{bd}+T_{bd}g_{ac}-T_{ad}g_{bc}-T_{bc}g_{ad}$ for $$T_{ab}=R_{ab}-\frac{R}{4}g_{ab}?$$

What I thought:
I know that $R_{ab}=g^{mn}R_{namb}=g^{mn}(T_{nm}g_{ab}+T_{ab}g_{nm}-T_{nb}g_{am}-T_{am}g_{nb})$, but how do I continue from here?