ATHENS, Greece—At least six people died and more than a dozen were believed missing after a migrant boat capsized in the Aegean Sea late Friday, bringing to at least 20 the combined death toll from three accidents in as many days involving migrant boats in Greek waters. The sinkings came as smugglers increasingly favor a perilous route from Turkey to Italy, which avoids Greece’s heavily patrolled eastern Aegean islands that for years were at the forefront of the country’s migration crisis. The coast guard said 57 people were rescued in Friday’s deadly incident after a sailboat capsized some 5 miles off the island of Paros, in the central Aegean. Survivors told the coast guard that about 80 people had been on the vessel. Five coast guard patrol boats, nine private vessels, a helicopter and a military transport plane continued the night-time search for more survivors, authorities said, while coast guard …