I'm in a bit of a quandry about when to take any sleep aid for an upcoming trip. I don't sleep well on planes either, but we'll be travelling in first class all the way.

Here's our schedule and I'd like to ask when would be the best time/flight to take a sleep aid:
LAX-MIA 6:45am-2:27pm
MIA-LHR 5:30pm-7:00am next day
LHR-NBO 10:10am-9:20pm

I wouldn't take it on the LAX-MIA flight, and might probably sleep for an hour anyway due to having to get up extra early. It seems as though the MIA-LHR flight would warrant taking a sleep aid, but it'll only be 2:30pm my body-clock time when the plane takes off. I would take it on the LHR-NBO portion, but we arrive at 9:20pm, so then I might not be able to sleep when it's bedtime in Nairobi. Or, not take it at all on any of the flights and take it once we get checked in to the Hilton Nairobi. You see my qandry? What would you do?