The deployment of multi-antenna systems with software defined reconfigurable beam patterns can potentially benefit vehicle-to-vehicle (V2V) communications by increasing the channel coherence time. This in turn necessitates an accurate characterization and modeling of the angular statistics of vehicular radio propagation environments. This work proposes an improved three-dimensional (3-D) spatial description of vehicular propagation environments and derives the closed-form analytical expressions for the joint and marginal statistics of the 3-D angle-of-arrival (AoA) and angle-of-departure (AoD). Then, based on the proposed geometric channel model, the AoA and AoD angular spreads are quantified in terms of the joint angular spread, elevational constriction, and the azimuthal constriction. These considered quantifiers are shown to be of high significance in quantification of angular spread in V2V radio propagation environments. The impact of various physical parameters on the angular spread is also investigated. These parameters include the link-distance, scattering volume, and the number of scatterers along the azimuth and elevation axes. The derived analytical expressions are also validated by simulations.