Combine squash, vinegar, oil, and 1/4 teaspoon salt in a large bowl; toss well to coat. Arrange squash mixture in a single layer on a jelly-roll pan coated with cooking spray.
Bake at 475 for 25 minutes or until tender and lightly browned, stirring occasionally.
While squash bakes, cook pasta according to the package directions, omitting salt and fat.
Drain in a colander over a bowl, reserving 1 tablespoon cooking liquid.
Melt butter in a large nonstick skillet over medium heat.
Add pine nuts, sage, and garlic; cook 3 minutes or just until the pine nuts begin to brown, stirring occasionally.
Place pasta, reserved cooking liquid, pine nut mixture, and squash mixture in a large bowl; toss gently to combine.
Add remaining 1/4 teaspoon of salt, arugula, cheese, and black pepper; toss gently to combine.