A new algorithm for 3D localization in multiplat-form radar networks, comprising one transmitter and multiple receivers, is proposed. To take advantage of the monostatic sensor radiation pattern features, angular constraints are imposed in the target localization process, restricting the azimuth-elevation location of any illuminated target. This is formulated as a non-convex constrained Least Squares (LS) optimization problem globally solved in a quasi-closed-form leveraging Karush-Kuhn-Tucker (KKT) conditions. The performance of the new algorithm is assessed in terms of the Root Mean Square Error (RMSE) and compared with the benchmark Root Cramer Rao Lower Bound (RCRLB) and some competitors from literature. The results corroborate the effectiveness of the new strategy which is capable of ensuring a lower RMSE than the counterpart methodologies especially in the low Signal to Noise Ratio (SNR) regime.