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The three-dimensional Gaussian beam transmission through a ferrite-semiconductor multilayer structure in the Faraday geometry is considered. The beam field is represented by an angular continuous spectrum of plane waves. In the long-wavelength limit, the studied structure is described as a gyrotropic medium defined by the effective permittivity and effective permeability tensors. The investigations are carried out in the frequency band where the real parts of the diagonal elements of both the effective permittivity and permeability tensors are close to zero. In this frequency band the studied structure is referred to a gyrotropic-nihility medium. It is found out that a Gaussian beam can pass through such a system practically without any distortion.