Student or Learner
i have to be taking tea?
i have had to take tea?
i had to be taking tea?
i had had to take tea?
i would have had to take tea?
To take tea is simply another way to say, 'to have tea', or 'to drink tea.'
In AmE, it sounds a bit old-fashioned and formal, but I don't know about BE.
All of your sentences are variations on the sentence, 'I have to take tea.' ('I must take tea.')Each sentence is in a different tense. Some of them sound awkward to me.
Also, 'I have to take tea,' sounds a bit odd, too, since having tea is usually considered a pleasurable experience. I suppose it would make sense if the complete sentence were, 'I have to take tea with my boring cousin tomorrow,'
I hope this is helpful,
Thanks for your kind words.
No, 'taking' isn't always negative. People 'take' baths, vacations, care, medicine, advice, 'five'(a short rest break), taxis, bows (on stage when the audience is applauding) and walks, as well as exams and 'lumps' (punishment or other unpleasant consequences).