Preheat the oven to 450°F (232°C). Lightly brush a large rimmed baking sheet with the olive oil.
Make the sauce: in a small saucepan over medium heat combine the Coca-Cola, ketchup, salt, cumin, crushed red pepper, garlic powder, and onion powder. Stir and simmer, stirring every few minutes, until the mixture reduces and thickens to a barbecue-sauce consistency.
Spatchcock the chicken: place the chicken breast-side-down and locate the backbone. Use kitchen shears to cut along one side of the backbone from neck to tail, then along the other side to remove the backbone completely.
Open the chicken and press to find the breastbone; make a shallow cut through the flexible breastbone cartilage (not all the way through the meat) so the bird can be flattened.
Flip the chicken breast-side-up on the prepared baking sheet and press down on the breasts to flatten. Arrange the drumsticks down and together and either remove wing tips or tuck them under the breasts to prevent burning.
Pat the chicken dry with paper towels, removing any excess juices from the baking sheet. Brush half of the prepared sauce over the chicken.
Roast the chicken in the preheated oven for 20 minutes.
Remove the chicken and brush with the remaining sauce. Return to the oven and roast an additional 15–30 minutes, until the internal temperature reaches 165°F (74°C) at the thickest part of the breast. (Total roast time will vary by bird size.)
Let the chicken rest a few minutes before slicing and serving.
