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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _derive_stereographic():
 """Compute the formulae to cut-and-paste into the routine below."""

    from sympy import symbols, atan2, acos, rot_axis1, rot_axis3, Matrix
    x_c, y_c, z_c, x, y, z = symbols('x_c y_c z_c x y z')

    # The angles we'll need to rotate through.
    around_z = atan2(x_c, y_c)
    around_x = acos(-z_c)

    # Apply rotations to produce an "o" = output vector.
    v = Matrix([x, y, z])
    xo, yo, zo = rot_axis1(around_x) * rot_axis3(-around_z) * v

    # Which we then use the stereographic projection to produce the
    # final "p" = plotting coordinates.
    xp = xo / (1 - zo)
    yp = yo / (1 - zo)

    return xp, yp