In eq. 4 of https://arxiv.org/abs/hep-th/9508128 it is stated that the Gauss-Bonnet term for gravity in 4d can be written as $$ S=\frac{1}{4}\int d^{4}x\,\epsilon^{\mu\nu\alpha\beta}\epsilon_{abcd}R_{\mu\nu}^{\quad ab}R_{\alpha\beta}^{\quad cd}\,, $$ in the tetrad formalism, with $\epsilon$ Levi-Civita tensor and $R$ Riemann tensor. In general this term is defined in a different way, as $$ S\propto\int d^{4}x\sqrt{-g}\left(R^{2}-4R^{\mu\nu}R_{\mu\nu}+R^{\mu\nu\alpha\beta}R_{\mu\nu\alpha\beta}\right)\,, $$ more common in the metric formulation of gravity (see eq. 7 in https://dx.doi.org/10.1088/1361-6382/ac500a).
How to prove that the two terms are identical? Is there any identity for the product $$ \epsilon^{\mu\nu\alpha\beta}\epsilon_{abcd}\,, $$ that helps in proving this equivalence?
