  Phase reduction is a dimensionality reduction scheme to describe the dynamics
of nonlinear oscillators with a single phase variable. While it is crucial in
synchronization analysis of coupled oscillators, analytical results are limited
to few systems. In this letter, we analytically perform phase reduction for a
wide class of oscillators by extending the Poincar\'e-Lindstedt perturbation
theory. We exemplify the utility of our approach by analyzing an ensemble of
Van der Pol oscillators, where the derived phase model provides analytical
predictions of their collective synchronization dynamics
