I'm going to elaborate on my unpopular opinion that Langdon isn't obligated to apologize to Santos.
Let's start by clarifying that drug addiction, whether to drugs, alcohol, or any other type of substance, is an illness, and it's an incurable illness. Once you're addicted, you'll always be addicted. You can control it, but you always run the risk of relapse. That doesn't make you evil or anything; it just makes you sick. That doesn't excuse your actions. That doesn't justify the fact that when he yelled at Santos in season one, it was cruel, humiliating, and incredibly unprofessional. Nothing justifies that.
But let's also clarify—and I say this with great affection for the character of Santos, whom I believe is one of the best—that Santos is exactly like Frank: arrogant, impulsive, and confident. The difference between Frank and Santos is that while Frank's arrogance and confidence stemmed from four years of experience as a resident physician, Santos had only been there a couple of hours and wanted to prove herself, which isn't inherently wrong, but she was impulsive, and it was her first day on the job. Frank didn't have to yell at her like he did, but he should have stopped her, and I don't judge him for that. You can't play the impulsive god to prove something when you have patients' lives in your hands.
Now, regarding forgiveness: Frank owes Santos an apology for treating her badly when he could have corrected her in a less aggressive way. However, Frank isn't obligated to apologize. Forgiveness must come from the heart and from a genuine desire to apologize; it shouldn't come from taking steps toward recovery or trying to fix what you did during your addiction. It's also understandable that Frank might only want to apologize to the people who are truly important to him, like Robby or Dana, because he's known them for years, or even Mel, with whom he formed a connection the day they met, or Louie, who was his patient and whose addiction he saw reflected in him.
But Trinity isn't someone Frank has known for a long time; he didn't develop a close friendship or camaraderie with her, nor was she his patient whose struggles he affected. Santos is the impulsive student he only saw once in his life, and it was during, quite literally, the worst day of his life because he had to deal with his addiction, which truly separated him from the people he loves and admires.
And if Frank doesn't genuinely want to apologize to Santos, why should he force himself? Santos, who is already hostile towards him, won't benefit from a perfunctory apology, and Frank won't benefit from a perfunctory apology either.
And we shouldn't force Santos to literally go through the process of getting an apology from someone she clearly doesn't want around. She's hostile, even to the point of being unprofessional, because she feels trapped. I'm not justifying her behavior because she has a foolish, childish, and unprofessional attitude, but I understand her. I wouldn't want to be around someone who treated me badly either. But unfortunately, in the hospital hierarchy, Frank is Santos's superior, and Langdon's job is to teach residents who are below him, like Trinity.
And if Langdon really doesn't care about apologizing to Trinity, that's COMPLETELY VALID. Trinity isn't important in Frank's life, just as Frank shouldn't be important in Trinity's. We know Trinity is deeply affected by how life has treated her, but it's valid for Frank not to care about apologizing to her, and that doesn't make him evil.
Really, there's no point in apologizing if it's not genuine and the person isn't important in our lives. It's part of growing up to know when it's truly worthwhile to apologize to people who aren't important in our lives.
I maintain that Frank owes Trinity an apology, but it's not wrong if he doesn't give it.