The puzzle on the relation between principle of special relativity and cosmologi cal principle, as well as the Beltrami-de Sitter-Lu puzzle on de Sitter/anti-de Sitter spacetimes in Einstein's framework of relativity are analyzed. It i s possible to generalize the principle of special relativity to the spacetimes w ith constant curvature and to establish the kinematics and particle dynamics for the special relativity in de Sitter/anti-de Sitter spacetimes with Beltrami met ric. In such a Beltrami system by the Beltrami coordinate simultaneity is just a n inertial system, the corresponding observers are inertial observers, the inert ial law is valid for test particles and light signals, and observables can be we ll defined which conserve and satisfy the generalized Einstein's formula. In addition to the Beltrami coordinate simultaneity there is also the proper-time simultaneity for the comoving observations and thus the Beltrami metric is trans formed into the Robertson-Walker-like metric which gives a closed 3-dimensional space and its deviation from flatness is of the order of cosmological constant. Therefore, it turns out that in such a kind of special relativity the relativity principle has an intrinsic affiliation with the “perfect” cosmological princi ple and without any puzzle. Furthermore, based on the recent astronomical observ ations, the Mach's principle is restated and it is showed that the cosmologi cal constant acts just as an origin of inertial motions in the de Sitter-invaria nt special relativity on Beltrami-de Sitter spacetime.