Cut peel including all white pith from each fruit with a sharp paring knife. Cut each segment from each fruit free from membranes. Halve grapefruit segments crosswise and transfer pieces to a bowl.
Stir in coconut, Campari, sugar, and just a pinch of salt. Refrigerate, covered, at least 15 minutes or up to 4 hours.
Just before serving, stir in nuts.
Makes 4 servings.
* Campari is a bitter Italian aperitif made according to a secret recipe originally developed in 1860 by Gaspare Campari in Milan. It is a bright pale cherry-pink color.