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/// Parallactic angle
///
/// Parallactic angle for a given hour angle and declination.
///
/// This function is part of the International Astronomical Union's
/// SOFA (Standards of Fundamental Astronomy) software collection.
///
/// Status: support function.
///
/// Given:
/// ```
/// ha double hour angle
/// dec double declination
/// phi double site latitude
/// ```
/// Returned (function value):
/// ```
/// double parallactic angle
/// ```
/// Notes:
///
/// 1) All the arguments are angles in radians.
///
/// 2) The parallactic angle at a point in the sky is the position
/// angle of the vertical, i.e. the angle between the directions to
/// the north celestial pole and to the zenith respectively.
///
/// 3) The result is returned in the range -pi to +pi.
///
/// 4) At the pole itself a zero result is returned.
///
/// 5) The latitude phi is pi/2 minus the angle between the Earth's
/// rotation axis and the adopted zenith. In many applications it
/// will be sufficient to use the published geodetic latitude of the
/// site. In very precise (sub-arcsecond) applications, phi can be
/// corrected for polar motion.
///
/// 6) Should the user wish to work with respect to the astronomical
/// zenith rather than the geodetic zenith, phi will need to be
/// adjusted for deflection of the vertical (often tens of
/// arcseconds), and the zero point of the hour angle ha will also
/// be affected.
///
/// Reference:
/// Smart, W.M., "Spherical Astronomy", Cambridge University Press,
/// 6th edition (Green, 1977), p49.