Proof of identity between Levi-civita and Kronecker delta using isotropy and symmetry

Question

I know the proof of the relation \begin{equation} \epsilon_{ijk}\epsilon_{ilm} = \delta_{jl}\delta_{km} - \delta_{jm}\delta_{kl} \end{equation} from different perspectives. Can anyone help me prove it by using the concept -isotropy and symmetry? How can I expand $ \epsilon_{ijk}\epsilon_{ilm} $ by using isotropic property? I know $ \epsilon_{ijk}\epsilon_{ilm} $ is a $4^{\text{th}}$ rank tensor. So I can expand it by the combination of two multiplied Kronecker deltas. But after expanding how can I use contraction to reach the result?