This code is intended to plot a cone projection but the result is self-inconsistent (it is a drawing of a cone but not a projection). Improve it to represent actual projection of a 3-dimensional cone with given parameters. 

# Define cone parameters
cone_top = SkyCoord('7h28m43s 69d11m24s', frame='icrs')  # Cone top (apex) as SkyCoord
cone_base_center = SkyCoord('7h28m38s 69d12m28s', frame='icrs')  # Cone base center as SkyCoord
cone_opening_angle = 20 * u.deg  # Opening angle of the cone
cone_orientation = 5 * u.deg  # In-plane orientation angle
cone_inclination = 30 * u.deg  # Tilt relative to the plane of the sky

# Load WCS for the image (assumed to be already defined)
wcs = WCS(HD(h_ha))

def rotate_coordinates(x, y, angle):
    """Rotate coordinates by a given angle in degrees."""
    angle_rad = np.deg2rad(angle)
    x_rot = x * np.cos(angle_rad) - y * np.sin(angle_rad)
    y_rot = x * np.sin(angle_rad) + y * np.cos(angle_rad)
    return x_rot, y_rot

def cone_base_vertices(cone_base_center, radius, inclination, orientation, num_points=100):
    """
    Generate vertices for the cone's base, projected onto the sky.
    Inclination and orientation are applied to the base's projection.
    """
    angles = np.linspace(0, 2 * np.pi, num_points)

    # Initial circular base vertices before projection
    offsets_ra = radius * np.cos(angles) / np.cos(cone_base_center.dec.radian)
    offsets_dec = radius * np.sin(angles)

    # Apply inclination by scaling the DEC offsets (flattening the base ellipse)
    offsets_dec_inclined = offsets_dec * np.cos(inclination.to(u.radian))

    # Rotate the base by the orientation angle
    offsets_ra_rot, offsets_dec_rot = rotate_coordinates(offsets_ra, offsets_dec_inclined, orientation)

    # Convert to SkyCoord object for the cone base vertices
    base_vertices = SkyCoord(ra=cone_base_center.ra + offsets_ra_rot * u.deg,
                             dec=cone_base_center.dec + offsets_dec_rot * u.deg)
    return base_vertices

# Compute the base radius based on the cone's opening angle and distance from top to base
cone_base_radius = (np.tan(cone_opening_angle.to(u.radian)) * cone_base_center.separation(cone_top)).to(u.deg)

# Generate the base vertices after applying the inclination and orientation
cone_base = cone_base_vertices(cone_base_center, cone_base_radius.deg, cone_inclination, cone_orientation)

# Convert the top and base vertices from SkyCoord to pixel coordinates
ra_top, dec_top = (cone_top.ra+10*u.arcsec).deg, cone_top.dec.deg
ra_base, dec_base = cone_base.ra.deg, cone_base.dec.deg

# Use WCS to convert RA/Dec to pixel coordinates
cone_top_pix = wcs.all_world2pix(ra_top, dec_top, 0)
cone_base_pix = wcs.all_world2pix(ra_base, dec_base, 0)

# Plotting the cone projection
for a in fig.axes:
    # Plot the cone base (as a polygon)
    cone_base_polygon = Polygon(np.column_stack([cone_base_pix[0], cone_base_pix[1]]), closed=True, edgecolor='magenta', facecolor='none', lw=2)
    a.add_patch(cone_base_polygon)
    
    # Plot the cone sides (from top to base vertices)
    for bx, by in zip(cone_base_pix[0], cone_base_pix[1]):
        a.plot([cone_top_pix[0], bx], [cone_top_pix[1], by], color='magenta', lw=1, alpha=0.7)
    
    # Mark the cone apex
    a.scatter(cone_top_pix[0], cone_top_pix[1], color='red', s=100, marker='x', label="Cone Top")