Do not be vulnerable - Be prepared
Understand the source of the anger. they are not mad at you. They are upset with their situation or maybe something completely unrelated.
Re-introduce yourself. Show your sincerity of wanting to help by offering your name.
Use the caller's name frequently if possible. This will help diffuse anger
Do not offer excuses. Excuses tell the caller that you do not want to help.
If you have to transfer the call, let them know why the transferee is better suited to help them. Let them know the name of the person, if possible.