Angels right-hander Nick Tropeano has a torn elbow ligament

The Angels on Tuesday lost their third starting pitcher to a major elbow injury in 3 1/2 months when Nick Tropeano was diagnosed with a medium- to high-grade tear in his ulnar collateral ligament, an injury that will sideline the promising young right-hander for the rest of this season and, most likely, all of 2017.

Tropeano joined left-hander Andrew Heaney, who underwent elbow ligament-replacement surgery July 1, and ace Garrett Richards, who tore his UCL in May and could need surgery, on the disabled list and sent the Angels searching for clues for the rash of UCL tears this season.

Since Mike Scioscia took over as manager in 2000, only three Angels pitchers have had ligament-replacement surgery while with the club — Matt Wise in 2003, Michael Kohn in 2012 and Tyler Skaggs in 2014. (Jason Vargas, Tyler Chatwood and John Lackey all had the procedure within two years after leaving the Angels.)

“With so many back to back, we’re looking in the mirror,” Scioscia said before Tuesday night’s game against the Texas Rangers. “You definitely look internally. You analyze everything from the throwing program to how you monitor guys. We’ve been very healthy over the course of our time here.

“This might be a fluke thing, but naturally, you have to look from within to make sure that the process is correct. We’ve always been confident with it, but when you have injuries like this, naturally, you look to see if there’s any cause.”

Tropeano, who was 3-2 with a 3.56 earned-run average in 13 starts, was pulled from Monday night’s game after giving up four runs and three hits — home runs to Rougned Odor, Adrian Beltre and Mitch Moreland — in two innings.

Tropeano, 25, described his initial discomfort as “day-two soreness after a start … it wasn’t anything that was alarming to me.”

The results of Tuesday’s MRI test were jarring.

“It’s upsetting; it’s a tough blow to me,” Tropeano said. “Obviously, I want to be out there. I want to pitch. I want to help this team win, and it sucks. It’s a part of the game nowadays, I guess. It’s one of those things where you’ve got to stay positive until you get that diagnosis.”

Tropeano plans to consult another doctor or two before deciding a course of action. He will consider stem-cell therapy, which Heaney and Richards had, and platelet-rich plasma injections but knows that surgery, which requires a 12- to 18-month recovery, is a distinct possibility.

“As of now, we’re going to keep all options open,” Tropeano said. “Usually when you see [UCL] damage, Tommy John surgery is the course of action. Right now, we’re just defining the severity of the tear and seeing what action I can take.”

Scioscia said either Skaggs, who is nearing the end of a long rehabilitation from elbow surgery and a shoulder injury, or Jhoulys Chacin, who threw four scoreless innings in relief of Tropeano on Monday night, would replace Tropeano in the rotation.

Skaggs, who hasn’t pitched in the big leagues in nearly two years, was scheduled to start for triple-A Salt Lake on Tuesday, but the game against Iowa was rained out.

The game will be made up as part of a doubleheader Wednesday, with Skaggs scheduled to start the first game. Since the Angels are off Thursday and won’t need a fifth starter until next Tuesday in Kansas City, Skaggs could pitch at triple A and still have five days of rest before starting for the Angels.

Skaggs gave up one hit, struck out 14 batters and did not walk any in seven scoreless innings of his last triple A start in Omaha on Thursday night.

Tropeano’s injury will likely scuttle any plans the Angels had of trading Hector Santiago or Matt Shoemaker before the Aug. 1 nonwaiver trade deadline.

With Richards, 28, Heaney, 25, and Tropeano likely out for 2017, and the contracts of Jered Weaver and the injured C.J. Wilson expiring, Santiago, Shoemaker and Skaggs will be needed to form the bulk of the rotation next season.

“All we’re thinking about right now,” Scioscia said, “is 2016.”

mike.digiovanna@latimes.com

Twitter: @MikeDiGiovanna