This paper addresses the challenge of implementing Direction of Arrival (DOA) methods for indoor localization using Internet of Things (IoT) devices, particularly with the recent direction-finding capability of Bluetooth. DOA methods are complex numerical methods that require significant computational resources and can quickly deplete the batteries of small embedded systems typically found in IoT networks. To address this challenge, the paper presents a novel Unitary R-D Root MUSIC for L-shaped arrays that is tailor-made for such devices utilizing a switching protocol defined by Bluetooth. The solution exploits the radio communication system design to speed up execution, and its root-finding method circumvents complex arithmetic despite being used for complex polynomials. The paper carries out experiments on energy consumption, memory footprint, accuracy, and execution time in a commercial constrained embedded IoT device series without operating systems and software layers to prove the viability of the implemented solution. The results demonstrate that the solution achieves good accuracy and attains an execution time of a few milliseconds, making it a viable solution for DOA implementation in IoT devices.