This research aims to accurately estimate the nine parameters of the three-diode photovoltaic model (3DM) by employing a hybrid optimization strategy that integrates the atan-sinc optimization algorithm (ASOA) with the Newton-Raphson method (NRM). The ASOA, inspired by the mathematical properties of the arctangent and sinc functions, serves as a population-based metaheuristic to generate candidate parameter sets for the comprehensive 3DM. To ensure a precise evaluation of each candidate, the NRM is entrusted with solving the complex transcendental equations typically associated with photovoltaic cell modeling, enabling a reliable computation of the objective function. The parameter estimation process is guided by experimental current-voltage (I-V) and power-voltage (P-V) curves collected from both monocrystalline and polycrystalline solar modules, which help to validate the robustness of the proposed methodology. The results demonstrate that the ASOA effectively explores the parameter space, while the NRM guarantees high accuracy with regard to solution evaluation, thereby producing dependable parameter estimates. All computational procedures and analyses were performed using MATLAB R2025b.