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

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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?
asked Dec 17, 2014 in Theoretical Physics by Outlander (95 points) [ no revision ]
The first formula can't be right, LHS has two residual indices, RHS has none.

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