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Ultra-wide coverage is one of the important concepts of the sixth generation (6G) mobile communications. High-altitude platform stations (HAPSs) have attracted considerable attention as a leading candidate for coverage extension of cellular networks. HAPSs should share a frequency band with terrestrial cellular networks and provide users with mobile communication services using the common frequency band to improve spectral efficiency in service links. However, the signals from HAPS strongly interfere with terrestrial cells in the service area of HAPS, which leads to a considerable deterioration in the system capacity of terrestrial cells. This study proposes a novel two-stage precoding scheme that realizes spectrum sharing between HAPS and terrestrial networks. The proposed scheme mitigates HAPS interference with terrestrial cells using beamforming techniques in phased array antenna systems. In the first stage, nulls are created in directions of terrestrial cells. In the second stage, user-specific beams are formed in directions of users connected to HAPS. Results demonstrate that the proposed scheme improves the signal-to-interference-plus-noise ratio of users in terrestrial cells by up to 10 dB compared with a conventional minimum mean square error (MMSE) precoder without nullforming when the HAPS uses a cylindrical array antenna with 196 elements. Furthermore, for ten terrestrial cells, the proposed scheme achieves 128% of total capacity of the conventional MMSE precoder. Total capacity is defined as the sum capacity of HAPS and all terrestrial cells.