Perhaps, to clarify a bit, you could define three different terms: happiness, contentment, and pain. To me, these three terms have very different meanings: happiness is a chemical produced in your brain, contentment is your brain (or perhaps soul) accepting its current circumstances, and pain is the physical kind.
Since these three terms are defined by seemingly independent concepts, it is thus possible to be both unhappy and in pain, yet still content with life. However, life is tricky indeed: both unhappiness and pain are ameliorated once you become content enough. Thus, it is not pain-avoidance that causes happiness, but pain-acceptance that causes contentment, which in turn causes you to be happy.
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