Ideally, you should keep a sleep journal for 30 days before you try to change anything about your sleep habits. As to the actual experiment don't drink any tea/coffee/colas for 30 days and see how it effects your sleep patterns.
PS: And I do mean zero for the full 30 days if you have any caffeine you have to start over.
Drinking tea is part of the culture of my family, so I started drinking it at a very young age (as soon as I could hold a cup?) with 3/4 milk and 1/4 tea. As I got older, the amount of tea increased until there was no milk left. These days, whoever I visit, it seems I can always count on being offered a cup of tea.
When I started having all sorts of issues sleeping at a young age, it just didn't occur to me or anyone that it could be the copious amounts of tea. Doctors ran tests on my blood numerous times and didn't find anything. They asked me all sorts of questions (even if I was pregnant at the tender age of 15, which shocked young innocent me), but caffeine never came up. Strangely, sending me to bed earlier resulted in tossing and turning even longer into the wee hours of the morning. Sleeping pills just resulted in feeling strangely dazed, but still not sleeping.
These days I have stopped drinking tea/caffeine after a certain hour in hopes of getting more sleep, but I still drink a cup of coffee in the morning and I still have troubles getting to sleep (takes a couple of hours no matter hour exhausted I feel). Maybe it's time to cut out the caffeine completely.
PS: And I do mean zero for the full 30 days if you have any caffeine you have to start over.