Remove the packet of giblets from the body cavity of the duck and set aside for another use. Remove and discard the fat just inside the body and neck cavities. Rinse the duck, inside and out, under cold running water and then drain and blot dry, inside and out, with paper towels. Prick the duck skin all over with a sharp fork, like a carving fork, taking care not to pierce the meat. Place the duck on a wire rack on a tray in the refrigerator and let dry out, uncovered, overnight (this is optional, but it will help give you crisper skin).
Pop the tab off the beer can, pour out three quarters of the beer (1 1/2 cups), and reserve for another use. If cooking the duck on the can, using a church key-style opener, make 2 additional holes in the top of the beer can. Using a funnel, add 1/2 cup orange soda to the beer can. Don't worry if the beer foams up a bit: This is normal. Reserve the remaining orange soda for the sauce.
Season the body and neck cavities of the duck very generously with salt and pepper. Place a strip of orange zest in the body cavity and in the neck cavity. Rub the outside of the duck all over with the cut orange. Drizzle 1 1/2 teaspoons of olive oil over the duck and rub it all over the skin. Very generously season the outside of the duck with salt and pepper.
If cooking on a can: Hold the duck upright, with the opening of the body cavity at the bottom, and lower it onto the beer can so the can fits into the cavity. You'll need to do some twisting. Pull the duck legs forward to form a sort of tripod so the bird stands upright. The rear leg of the tripod is the can. If cooking on a roaster: Fill it with1/2 cup beer and 1/2 cup orange soda and position the duck on top, following the manufacturer's instructions.
Tuck the tips of the wings behind the duck's back.
Set up the grill for indirect grilling and preheat to medium. If using a charcoal grill, place a large drip pan in the center. When ready to cook, carefully stand the duck up in the center of the hot grate, over the drip pan and away from the heat. Cover the grill and cook the duck until the skin is a dark golden brown and very crisp and the meat is cooked through (about 180°F on an instant-read meat thermometer inserted in the thickest part of a thigh, but not touching the bone), 11/2 to 2 hours. After 1 hour, prick the duck skin again with a sharp fork, taking care not to pierce the meat. This helps release the fat. Baste the duck with the remaining 11/2 teaspoons of olive oil, taking care not to knock the bird over. If using a charcoal grill, you'll need to add 12 fresh coals per side after 1 hour. If the duck skin starts to brown too much, loosely tent the bird with aluminum foil.
If cooking on a can: Using tongs, hold the duck by the can and carefully transfer it in an upright position to a platter. If cooking on a roaster: Use oven mitts or pot holders to remove the duck from the grill while it's still on the vertical roaster.
Present the duck to your guests. Let the duck rest for 5 minutes, then carefully lift it off the support. Take care not to spill the hot beer or otherwise burn yourself. Carve the duck or cut it in half or quarters and serve with Apricot-Orange Sauce.
Note: Because of the duck's elongated shape, you'll need a "tall boy"-a 16-ounce can of beer.