limit tan(t) as t->pi/2 from the left - Wolfram|Alpha
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Series expansion at t=π/2:

link to /input/?i=-1%2F%28-%CF%80%2F2%2Bt%29%2B1%2F3+%28-%CF%80%2F2%2Bt%29%2B1%2F45+%28-%CF%80%2F2%2Bt%29%5E3%2B2%2F945+%28-%CF%80%2F2%2Bt%29%5E5&lk=1&a=ClashPrefs_*Math-
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