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I do not know if this is a rhetorical question, but I believe that these two concepts are mutually inclusive. Happiness and loneliness can coexist in many ways within an individual without one being dominant over the other. Happiness is intimate, and in this sense, it could be called lonesome. Still, happiness can also be a shared event (e.g., being happy for your son's achievement or your girlfriend's joy). On the other hand, the mystic monk on top of the mountain can be content with being alone. Thus, happiness can be reflected in loneliness too. The beneficial or destructive attitudes of either emotion (or its composite) will depend on the focus an individual assigns to each. Humans are a complicated species. Best Regards, @fcpway

your answer was more than good. it was a while I haven't read such good description of happiness.

I have been alone in many period of times in my life, and I believe loneliness doesn't work for me... I never found happiness in being alone, but I admit many people are happier in their solitude