This paper presents a novel antenna configuration to measure directions of multiple signal sources at the receiver in a THz mobile network via a single channel measurement. Directional communication is an intrinsic attribute of THz wireless networks and the knowledge of direction should be harvested continuously to maintain link quality. Direction discovery can potentially impose an immense burden on the network that limits its communication capacity exceedingly. To utterly mitigate direction discovery overhead, we propose a novel technique called spectrum shaping capable of measuring direction, power, and relative distance of propagation paths via a single measurement. We demonstrate that the proposed technique is also able to measure the transmitter antenna orientation. We evaluate the performance of the proposed design in several scenarios and show that the introduced technique performs similar to a large array of antennas while attaining a much simpler hardware architecture. Results show that the spectrum shaping with only two antennas placed 0.5 mm, 5 mm, and 1 cm apart performs direction of arrival estimation similar to a much more complex uniform linear array equipped with 7, 60, and 120 antennas, respectively.