( The post references the reader as 'you'; it may seem to be a 'lesson' or a 'lecture', but then I couldn't put it in a better way. )
opinion noun view held as probable.
belief noun what one accepts as true.
fact noun thing known to exist as true or reality.
I know I (as a non-GRE student) can't precisely spell out which one is 'stronger' and things like that, but then I have somewhat undestood how to differentiate between them. Rather, more importantly, we need to know why to differentiate these. Everyone holds an opinion about almost everything; when his opinion grows stronger, he starts believing in it; and if his beliefs are proven (by earlier-know facts, of course), then his belief transforms into a fact. People 'give; opinions, 'express' beliefs and 'state' facts. That's why it is essential not to mix up the three. I have found people being affected by others' opinions or adapting to others' beliefs. I believe (note the verb), that we must accept others' opinions; think over their beliefs; and adapt ourselves to the facts. Remember that facts are universal and do not need an 'adjective' (his/their) even in English usage, which simply proves the difference.
Some say that if you don't care for others' opinions, then you are arrogant or egoistic. But then, you should just listen to them, analyse them and then try to find out whether the opinion is valid (even before thinking about their usefulness). Similarly, beliefs are also to be thought about, more rigorously and then taken into consideration. But facts are facts. Beliefs can become facts, only after they are proven, by logically reasoning it out. 'A theorem is a fact, but only after if it has valid proof'. But remember any wrong assumption can prove the whole theorem wrong. If you yourself can reason out others' beliefs/opinions then it becomes a fact for you and NOW you need to think about applying the fact. You need not prove a fact's validity but test their usefulness or relevance.Relevance is very important, because we very easily associate any negative quality of ours with our failure. Any effect is present onky dueto some of the causes not all (80:20 Pareto's principle :)). The software engineers should now understand why a fish-bone diagram is so important in debugging.
During many incidents that have taken place with me or around me, I have found people trying to confuse between the three and that has become the major concern. People take others' opinions to their heart and that affects their life so much that they don't even think twice. The Joshua experience of my friends was one of them. ( for all those in the dark, this is some anon guy posting some nasty things about people on orkut.) It's simple. He can't prove it,that's why he's anon. Which means whatever he says, is just an opinion. Look within yourself. If you feel even a bit of truth in his 'opinions' then worry about it. Else go on with your life. And this is what I feel is extremely essential for any team to work together. But remember, you need objectivity in your thinking for deciding the validity of opinions. Else, you will be one more arrogant guy, who doesnt change himself for anything in this world. And remember, all that I said is just my 'belief'. Yes, ther is some reasoning behind this, but then, unless and until it is universally accepted, you still need to think about this before accepting these comments.