  The Gibbons-Werner method for calculating deflection angles using the
Gauss-Bonnet theorem and optical/Jacobi metric has become widely popular in
recent years. Werner extended this method to stationary spacetimes, where the
optical/Jacobi metric takes the form of a Finsler metric of Randers type, by
adopting an osculating Riemannian metric. Werner's method is significant as it
provides a concise expression for the deflection angle, retains applicability
for gravitational lensing in Finsler geometry beyond the Randers type, and has
the potential to stimulate widespread application of Finsler geometry across
diverse fields. However, because of the cumbersome calculations required in
Werner's method using conventional coordinates $(r,\phi)$, it has not been
widely adopted. The aim of this paper is to alleviate the computational burden
associated with Werner's method. To this end, we introduce Cartesian-like
coordinates $(X,Y)$ to construct the osculating Riemannian metric and calculate
the deflection angle using the Gauss-Bonnet theorem. We illustrate the current
method with examples of the deflection of massive particles in Kerr spacetime,
rotating Bardeen (Hayward) regular spacetime, and Teo rotating wormhole
spacetime, respectively.
