The glasswing butterfly (Greta oto) has, as its name suggests, transparent wings with remarkable low haze and reflectance over the whole visible spectral range even for large view angles of 80°. This omnidirectional anti-reflection behaviour is caused by small nanopillars covering the transparent regions of its wings. In difference to other anti-reflection coatings found in nature, these pillars are irregularly arranged and feature a random height and width distribution. Here we simulate the optical properties with the effective medium theory and transfer matrix method and show that the random height distribution of pillars significantly reduces the reflection not only for normal incidence but also for high view angles.