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Relativistic jets launched by Active Galactic Nuclei (AGN) are observed across the entire electromagnetic spectrum, from radio wavelengths up to very high-energy gamma-rays, and are emerging as sources of high-energy neutrinos. Despite the pivotal role of AGN jets in astronomy, we have no reliable model for the origin of the non-thermal radiation. AGN jets are most likely magnetically dominated (i.e., the available magnetic energy per particle largely exceeds the rest mass energy), and naturally become turbulent. The dissipation of the jet's magnetic energy by a turbulent cascade accelerates particles to ultrarelativistic velocities. These particles can power the observed non-thermal radiation via synchrotron and inverse Compton cooling. The advent of large scale Particle-In-Cell simulations makes it possible to study the radiative turbulent cascade from first physical principles. I will show that particles accelerated by magnetically dominated turbulence have a strong pitch angle anisotropy, i.e. their velocity is nearly aligned with the local magnetic field. The pitch angle anisotropy suppresses the rate of synchrotron cooling, while the rate of inverse Compton cooling remains unchanged. This effect was not considered in previous theoretical models of AGN jets, yet it is crucial to infer the physical properties of AGN jets by modelling the non-thermal radiation. I will show that simultaneous multiwavelength observations of AGN flares can be used to probe the pitch angle anisotropy of the radiating particles.