You can not get angles from a single point. If you need spherical coordinates of the XYZ point in Cartesian, you can just apply a transform (see Wiki or Wolfram). Otherwise, you need the second point to measure the angle.
I may guess you might want the initial direction vector of the particle, which is taken from the generator
const auto generatorAction = dynamic_cast<const PrimaryGeneratorAction *>(G4RunManager::GetRunManager()->GetUserPrimaryGeneratorAction());
auto particle_direction = generatorAction->GetParticleGun()->GetParticleMomentumDirection();