Cuticles of some Chrysina scarabs are characterized by flat, graded, and twisted structures of nanosized chitin fibrils. As inferred from SEM images, each species has its own spatial period or pitch P which is dependent on the depth z through the cuticle. From Berreman's formalism, taking into account the corresponding P(z) dependence, we evaluate reflection spectra of C. aurigans and C. chrysargyrea scarabs. The spectra display the main spectral features observed in the measured ones when small sections of the cuticles are illuminated with non-polarized light, for wavelengths between 300 and 1100 nm. By considering these twisted structures as 1D photonic crystals, an approach is developed to show how the broad band characterizing the reflection spectra arises from a narrow intrinsic photonic band width, whose spectral position moves through visible and near infrared wavelengths. The role of the epicuticle that covers the twisted structures is analyzed in terms of a waxy layer acting as an anti-reflecting coating that also shows low levels of light scattering.