Angle-of-arrival (AoA) information is vital for beamforming which is used to combat severe propagation loss in millimetre wave communications. Although blind AoA estimation has been extensively studied for digital array, few results were reported for hybrid array. Well known subspace-based methods such as MUSIC and ESPRIT have been successfully developed. However, their efficacy is reduced in hybrid array due to the loss of spatial degrees of freedom (DoFs). In this paper, we propose a method to solve the problem. The proposed algorithm uses an augmented beamspace approach and a precoding scheme such that the lost spatial DoFs can be recovered. As a result, MUSIC and ESPRIT can be used with full capacity. Theoretical analysis is conducted to obtain lower bounds of the estimation-error variances. Simulations with an OFDM system show that the proposed method can achieve satisfactory performance and the theoretical bounds are tight.