A technical question about the field strength tensor $F_{\mu \nu}$

Question

I would like to ask how can one show that $$F_{\mu \rho}\tilde{F}_{\nu}^{\,\, \rho}=\frac{1}{4}F_{\rho \sigma}\tilde{F}^{\rho \sigma}$$ for $D=4$. The dual field strength is defined as $\tilde{F}^{\mu \nu} = -\frac{1}{2}i\varepsilon^{\mu \nu \rho \sigma}F_{\rho \sigma}$. Any ideas?

Comments

The first formula can't be right, LHS has two residual indices, RHS has none.