Directional Radio Frequency (RF) / Free-Space-Optical (FSO) transceivers have the potential to play a significant role in future generation wireless networks. They are advantageous in terms of improved spectrum utilization, higher data transfer rate, and lower probability of interception from unwanted sources. Despite these advantages, communications using directional transceivers require establishment and maintenance of line-of-sight (LOS). Thus, establishment of the communication link or neighbor discovery plays an important role in mobile ad hoc networks with RF/FSO directional transceivers. We consider two nodes (Unmanned Aerial Vehicles (UAVs) or Quadcopters) hovering in 3D space, each with one directional transceiver mounted on a mechanically steerable spherical structure/head, with which they can scan 360 degrees in the horizontal plane and 360 degrees in the vertical plane. We propose a novel scheme that deals with the problem of automatic discovery and establishment of LOS alignment between these nodes. We performed extensive simulations to show the effectiveness of the proposed neighbor discovery method. The results show that, using such mechanically steerable directional transceivers, it is possible to establish communication links to similar neighboring nodes within minimal discovery times.