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Modern methods of remote sensing of the atmosphere and the surface are based on minimizing the difference between simulated and measured reflectances. An iterative process to specify the model of the atmosphere is used, and the direct problems to the radiative transfer equation (RTE) are solved on each iteration loop. These direct problems have to be solved quickly for realistic models of the atmosphere under peaked-forward scattering by aerosol particles, water droplets, and ice crystals. Accurate and fast algorithms to solve the RTE under these conditions are in great demand. A method based upon the new version of small angle approximation to the singular component of the solution is presented. Numerical results in the problem on reflection of the visible light by aerosol and cloud layers are presented. Calculation time reduction due to the small angular technique is shown. [ABSTRACT FROM AUTHOR]