We study 4d SU(N) pure Yang-Mills theory with a topological theta-angle. It has been a long standing problem to study the theta-dependence of the free energy, and to settle on the fate of the CP symmetry at theta=pi. In this talk we introduce a new lattice gauge theory technique called the "subvolume method", which demonstrates that the 4d SU(2) pure Yang-Mills theory at theta=pi has spontaneous CP breaking at zero temperature. This is consistent with the large N prediction, and indicates that the similarity between 4d SU(N) and 2d CP^{N−1} theories breaks down for N=2. We also discuss the temperature dependence of the theory.