The transmission and reflection of a monochromatic electromagnetic wave in a twisted nematic wedge are investigated. We consider the special case where the characteristic length xi of the director twist is much higher than the optical wavelength lambda. By using the perturbative theoretical procedure proposed by Oldano et al., we find an analytic expression for the transmitted and reflected beams at the first order in the perturbative parameter epsilon = 1/Delta k xi, where Delta k is the difference between the extraordinary and ordinary wavenumbers. The intensity and the polarization of the refracted and reflected beams are related by simple analytic expressions to the normal derivatives of the director at the interfaces and do not depend on details of the bulk director distortion. The theoretical predictions are compared with experimental results obtained using an electric field to twist the director-field A satisfactory agreement is found between theory and experiment. On the basis of our theoretical results we propose a simple experimental method to measure the twist viscosity coefficient of nematic liquid crystals.