As an aside, the whole "8 hour half-life" is astonishingly high, to me. Caffeine is nice, but it doesn't seem to have that strong an effect on me, and certainly nothing I notice 5-8 hours after. I drink quite a lot of caffeine these days, but even at times when I went off caffeine for a few weeks, I didn't get effect durations any longer than 1-3 hours.
Might have something to do with the strength of the tea, though.
I have the genes that extend caffeine half-life. If I drink an American large coffee, I get anxious. I can drink a whole pot or two of green tea and feel a nice lift in mood.
As others have mentioned, any coffee after noon and I can't fall asleep until around 2am. I avoid caffeine most days except for the occasional morning kombucha.
[1] https://www.reddit.com/r/nootropics/wiki/faq#wiki_l-theanine
Metabolism of drugs like caffeine is genetically quite variable and is quite an issue for pharmaceutical companies.
short summary: 200mg at 7 a.m., and going to bed at 11 p.m. had following effect: "Compared to placebo, sleep efficiency and total sleep time were significantly reduced."
The effects are 6 hours for me, less than 1 hour for my father (who smokes), and can last over 18 hours for my wife and mother-in-law.
I haven't seen the studies on caffiene half-life, but I suspect the variation is very high.
I personally take it early morning and after a siesta.
Green tea is less of a problem (then again, the way I prepare it, it contains much less caffeine).