class_docstr: Private class for the n-dimensional hypersphere.
  
  Class for the n-dimensional hypersphere embedded in the
  (n+1)-dimensional Euclidean space.
  
  By default, points are parameterized by their extrinsic
  (n+1)-coordinates. For dimensions 1 and 2, this can be changed with the
  `default_coords_type` parameter. For dimensions 1 (the circle),
  the intrinsic coordinates correspond angles in radians, with 0. mapping
  to point [1., 0.]. For dimension 2, the intrinsic coordinates are the
  spherical coordinates from the north pole, i.e. where angles [0., 0.]
  correspond to point [0., 0., 1.].
  
  Parameters
  ----------
  dim : int
      Dimension of the hypersphere.
  
  default_coords_type : str, {'extrinsic', 'intrinsic'}
      Type of representation for dimensions 1 and 2.
docstr: Compute the angle of a point in the plane.
  
  Convert from the extrinsic coordinates in the 2d plane to angle in
  radians. Angle 0 corresponds to point [1., 0.]. This method is only
  implemented in dimension 1.
  
  Parameters
  ----------
  point_extrinsic : array-like, shape=[..., 2]
      Point on the circle, in extrinsic coordinates in Euclidean space.
  
  Returns
  -------
  point_angle : array_like, shape=[..., 1]
      Point on the circle, i.e. an angle in radians in [-Pi, Pi].
docstr_tok: ["Compute","the","angle","of","a","point","in","the","plane",".","Convert","from","the","extrinsic","coordinates","in","the","2d","plane","to","angle","in","radians",".","Angle","0","corresponds","to","point","[","1.",",","0.","]",".","This","method","is","only","implemented","in","dimension","1",".","Parameters","--","--","--","--","--","point_extrinsic",":","array-like",",","shape=","[","...",",","2","]","Point","on","the","circle",",","in","extrinsic","coordinates","in","Euclidean","space",".","Returns","--","--","--","-","point_angle",":","array_like",",","shape=","[","...",",","1","]","Point","on","the","circle",",","i.e",".","an","angle","in","radians","in","[","-Pi",",","Pi","]","."]
code: def extrinsic_to_angle(point_extrinsic):
      """Compute the angle of a point in the plane.
  
      Convert from the extrinsic coordinates in the 2d plane to angle in
      radians. Angle 0 corresponds to point [1., 0.]. This method is only
      implemented in dimension 1.
  
      Parameters
      ----------
      point_extrinsic : array-like, shape=[..., 2]
          Point on the circle, in extrinsic coordinates in Euclidean space.
  
      Returns
      -------
      point_angle : array_like, shape=[..., 1]
          Point on the circle, i.e. an angle in radians in [-Pi, Pi].
      """
      return gs.expand_dims(
          gs.arctan2(point_extrinsic[..., 1], point_extrinsic[..., 0]),
          axis=-1,
      )
  
imports: import logging
  import math
  from itertools import product
  from scipy.stats import beta
  import geomstats.algebra_utils
  import geomstats.backend
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import get_batch_shape, repeat_out
label_desc: Use image node_id 9 for calling the _Hypersphere obj's underlying member method code with example usage: obj.extrinsic_to_angle(point_extrinsic) and returns: gs