Understand the person's intentions

Someone who is calm is seen as being in control, centered and more respectable. 

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.

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. 

When all else fails, escalate to your manager. 

If you have already tried everything and the person is still not being receptive, the best way might be to just ignore.

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.

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.

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.