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This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability and spectral efficiency (SE) in the presence of fluctuations of 3D antenna beamwidth. Within this analytical framework, the macro base stations (MBSs) are meticulously characterized through the application of an independent 2D homogeneous Poisson point process (PPP), while the low-altitude platforms (LAPs) are described using an independent 3D PPP. The study entails the derivation of association probabilities, determining the likelihood of the T-UE associating with MBSs, line-of-sight LAPs, and non-line-of-sight LAPs. Through rigorous mathematical analysis, the paper formulates precise analytical expressions that encapsulate the association and coverage probabilities, taking into account the inherent variability in the UAV antenna beamwidth. This research focuses on a thorough performance evaluation of the T-UE across diverse network configurations, encompassing LAP density, the transmission power of LAPs, and the critical signal-to-interference ratio threshold. The outcomes of this study distinctly underscore the substantial disruptive impact resulting from fluctuating beamwidth on the performance of the T-UE within the UAV-assisted cellular network. Additionally, this performance is further impacted by larger densities and transmission power of the LAP. Hence, it is imperative to take into account the influence of these fluctuations on …