This means you need a panel that can in the number of day light hours available to it, provide 3.75W * 24 hours = 90Wh per day.
So if you want to be able to have it full recharge in 1 hour, you need a panel that can provide 90W. If you expect 4 hours of good light per day, then you only need 22.5W.
But also remember that you won't likely get 100% of the panel's rated output.
If you live in a sunny area, about 50% is probably reasonable to expect, but remember that days on end of overcast weather will still be a problem. The solution there is to have your battery big enough to hold multiple days of power, i.e., n*90Wh, where n is the number of days you want.
In short, I'd recommend a 40W panel as a bare minimum for running 3.75W load, and ideally 180Wh or more of battery. I'd recommend LiFePO4 batteries as they last longer than either sealed lead-acid or LiPo, and unlike LiPo, aren't prone to bursting into flames and melting through concrete.
You then need a nice MPPT solar panel controller, and a good battery charge controller. Many cheap solar panels have low-efficiency panel controllers, that mean you get much less than the rated power in real life. This is why the new Mesh Extenders have built-in MPPT panel controller and multi-chemistry battery charger, so that you can just add a bare panel and bare batteries. The flip side is that the Mesh Extenders are (currently quite a lot) more expensive than a little GL-AR150.
BTW - Are you sure that the GL-AR150 uses that much power? Do you have a USB device connected to it? We have GL-AR150s in the lab, and they use a lot less than that, even with wifi running in ad-hoc. We see current consumption (without a USB device, but with one ethernet plugged in) of only around 160mA - 250mA, i.e., 0.8W - 1.25W. This means that you could get away with about 1/3 to 1/4 of the recommended values below. In fact, I just tested a Mesh Extender prototype PCB, and it consumes only about 200mA = 1W (without an RFD900 packet radio, to make it comparable with the GL-AR150). Thus I'd be surprised if the GL-AR150 was really using 0.75A. In fact, you have said your 12000mAh battery can run it for 3.5 days = 84 hours. Thus it is drawing an average of only 143mA from your battery, which backs up my measurements here.
So the good news is, you only need something quite a bit smaller that I calculated above. I'd recommend a 20W panel + 40Wh of battery as a starting point, provided you have efficient panel regulator and battery charger elements.
Paul.