I m going to travel from LA to Inchon via Beijing and on the way back from Inchon to LA.

I am an American wanting to fly from LA to Inchon, South Korea via Beijing and on the way back from Inchon to LA. benefit from the 72-hour visa-free transit by staying 3 nights in Beijing to see the national monuments (Great Wall of China, Temple of Heaven, etc). Do i qualify for the 72-hour free transit policy?