In this paper, we consider the problem of estimating the angular parameters, i.e., the nominal angle-of-arrivals (AoAs) and angular spreads, of incoherently distributed sources using the phased-array equipped with a single RF chain. We first derive the approximate Fourier series of the received power. The coefficients can be expressed in closed form with the angular parameters. In the case of single source, this finding directly suggests the design of the low-complexity algorithm that performs spatial sampling and discrete Fourier transform to estimate the Fourier series coefficients, from which the nominal AoA and angular spread can be obtained successively. In the case of multiple sources, we focus on one source at one time, and the multiples sources are handled one by one. Based on the Fourier series expression, the power fitting approach is proposed to build the nonlinear least-squares problem. Then, the semi-exhaustive search algorithm is developed to find the solution, which gives the angular parameters of the target source. Additionally, the approximate Cramer-Rao bound is derived as benchmark. The numerical results demonstrate that in certain cases, the proposed methods can even outperform the existing method that uses fully-digital array.