Iguazu doesn't need much of an angle, but it does need a plan. The river that rises near Curitiba runs along the Brazil-Argentina border and then drops off a basalt ledge in roughly 275 separate falls, and the two countries each own part of the view. Eleanor Roosevelt is said to have taken one look and sighed "Poor Niagara!" Brazil's national park exists largely because the aviator Alberto Santos-Dumont came in 1916, was floored, and leaned on the governor of Paraná. The park was created in 1939, and UNESCO listed the Argentine and Brazilian parks in 1984 and 1986.
Three days is the right length because the falls are really two day trips. The Brazilian side is the panorama: a trail along the cliff, a walkway over the water and a boat into the spray. The Argentine side is the immersion: a train, kilometers of catwalks, and most of the falls close enough to touch. Doing both properly takes two days, and the third goes to Itaipu, one of the biggest dams on Earth, and the spot where three countries meet. The river also runs the schedule: in high water the Devil's Throat walkways shut on both sides, and floods can keep them closed for days.
Day one is Parque das Aves and the Brazilian park, day two crosses the border to the Argentine park, and day three covers Itaipu, the Triple Frontier and an optional, honestly flagged look at Ciudad del Este. Start on a Wednesday. Weekends are the busiest days at the parks, the Marco das Três Fronteiras is closed on Mondays, the Rafain dinner show runs Monday to Saturday, and the mosque doesn't take visitors on Sundays. Foz is the easiest way into Brazil, with Argentina and Paraguay a bus ride away.