<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def sphdist (lat1, lon1, lat2, lon2):
 """Calculate the distance between two locations on a sphere. lat1 The latitude of the first location. lon1 The longitude of the first location. lat2 The latitude of the second location. lon2 The longitude of the second location. Returns the separation in radians. All arguments are in radians as well. The arguments may be vectors. Note that the ordering of the arguments maps to the nonstandard ordering ``(Dec, RA)`` in equatorial coordinates. In a spherical projection it maps to ``(Y, X)`` which may also be unexpected. The distance is computed with the "specialized Vincenty formula". Faster but more error-prone formulae are possible; see Wikipedia on Great-circle Distance. """

    cd = np.cos (lon2 - lon1)
    sd = np.sin (lon2 - lon1)
    c2 = np.cos (lat2)
    c1 = np.cos (lat1)
    s2 = np.sin (lat2)
    s1 = np.sin (lat1)
    a = np.sqrt ((c2 * sd)**2 + (c1 * s2 - s1 * c2 * cd)**2)
    b = s1 * s2 + c1 * c2 * cd
    return np.arctan2 (a, b)