import numpy as np
import healpy as hp
import matplotlib.pyplot as plt
dir1 = (112.66,65.74)
dir2 = (119.94,67.56)
distance = np.rad2deg(hp.rotator.angdist(dir1=dir1, dir2=dir2, lonlat=True))
print(f'{distance=}')
in `hp.ang2pix`, the longitude have no limits where latitude should range from -90 to 90.