I mixed what I thought was the correct gas/oil ratio (40 - 1) for a Weed Eater GTI 17T trimmer. The trimmer had some correct fuel mixture in the fuel system started worked until the new mixture was introduced. How can I determine if I correctly mixed the fuel? How do I clean out the mixture that's already in the trimmer.

You'd need a visgage, or some other kind of viscosity measuring device. Measuring the flash point may work... both require expensive equipment...

Use an old oil drain pan and remove the old fuel.