Grapefruit Cups with Wine Syrup

Cut peel and white pith from 6 grapefruit. Working over bowl, cut between membranes to release segments. Cover and chill segments at least 30 minutes and up to 1 day. Cut remaining 4 grapefruit in half. Using juicer, juice grapefruit. Pour 3/4 cup juice into heavy medium saucepan. (Reserve any remaining juice for another use.) Using spoon, scoop out membranes from grapefruit halves and discard, reserving grapefruit cups. Add wine and sugar to juice in saucepan. Stir over medium heat until sugar dissolves. Simmer until reduced by half, about 10 minutes. Cool wine syrup to room temperature. (Can be prepared 1 day ahead. Cover grapefruit halves and wine syrup separately and refrigerate. Bring wine syrup to room temperature before using.) Arrange grapefruit cups on large platter. Divide segments among cups. Drizzle each grapefruit cup with wine syrup and serve.