Structural colors in nature are frequently produced by the ordered arrangement of nanoparticles. Interesting examples include reptiles and birds utilizing lattice-like formation of nanoparticles to produce a variety of colors. A famous example is the panther chameleon which is even able to change its color by actively varying the distance between guanine nanocrystals in its skin. Here, we demonstrate that the application of rigorous electromagnetic methods is important to determine the actual optical response of such biological systems. By applying the Korringa-Kohn-Rostoker (KKR) method we calculate the efficiencies of the reflected diffraction orders that can be viewed from directions other than the specular. Our results reveal that important characteristics of the reflectance spectra, especially within the ultraviolet (UV) and short visible wavelengths region, cannot be predicted by approximate models like the often-applied Maxwell-Garnett approach. Additionally, we show that the KKR method can be employed for the design of multi-layer structures with a desired optical response in the UV regime.