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Simulation is often used to predict the response of gamma-ray spectrometers in technology viability and comparative studies for homeland and national security scenarios. Candidate radiation transport methods generally fall into one of two broad categories: stochastic (Monte Carlo) and deterministic. Monte Carlo methods are the most heavily used in the detection community and are particularly effective for calculating pulse-height spectra in instruments. However, computational times for scattering- and attenuation-dominated problems can be extremely long - many hours or more on a typical desktop computer. Deterministic codes that discretize the transport in space, angle, and energy offer potential advantages in computational efficiency for these same kinds of problems, but pulse-height calculations are not readily accessible. This paper investigates a method for coupling angular flux data produced by a three-dimensional deterministic code to a Monte Carlo model of a gamma-ray spectrometer. Techniques used to mitigate ray effects, a potential source of inaccuracy in deterministic field calculations, are described. Strengths and limitations of the coupled methods, as compared to purely Monte Carlo simulations, are highlighted using example gamma-ray detection problems and two metrics: (1) accuracy when compared to empirical data and (2) computational time on a typical desktop computer.