Get on your daily tasks and interface with the person only where needed.
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Connect with your colleagues on a personal level. Go out with them for lunches or dinners. Get to know them as people, and not colleagues. Learn more about their hobbies, their family, their lives. Foster strong connections. These will go a long way in your work.
In all likelihood, your colleagues, managers and friends must have experienced similar situations in some way or another. They will be able to see things from a different angle and offer a different take on the situation.
Acknowledge that the situation has already occurred.
Rather than harp on what you cannot change, focus on the actionable steps you can take to forward yourself in the situation.
Unless you know that anger will trigger the person into action and you are consciously using it as a strategy to move him/her, it is better to assume a calm persona.
If you are going to treat the person with disrespect, it's not going to be a surprise if he/she treats you the same.
Do unto others as you would have them do unto you.
Even when it may seem that the person is just out to get you, there is always some underlying reason that is motivating them to act this way.
Try to identify the person's trigger: What is making him/her act in this manner? What is stopping him/her from cooperating with you? How can you help to meet his/her needs and resolve the situation?
This is considered the trump card and shouldn't be used unless you've completely exhausted your means.
Letting them in on the reason behind your actions and the full background of what is happening will enable them to empathize with your situation.
This lets them get them on-board much easier.
Accept them exactly as they are.
Accept that they are unable to change, at least at this point in time. Unless you see real change — proof that this person is making an effort to listen and meet you halfway — you can assume that their behavior is what it has always been.