Doesn't sound like an example of a situation where nagging could occur... if the taking out of the garbage is urgent and thats the persons job then I agree you. You shouldn't need to ask them nicely but hey it always helps, why not?
Of course this is not what the thread is about, a better example would be "cleaning the garage" as there is no urgency in this. However to an SJ that asked you to do it, it would be
expected to be done and thats when said
nagging starts to occur
Now if I wanted someone I'm living with to clean the garage and lets say for example I had nothing to offer in return then I would defiantly be asking said person in a way that shows that you really need the help (maybe you are swamped with work, tell them)
If they AGREE don't just leave it at that and assume it will be done... two words...
time frame
If they agree, finish by saying it needs to be done
today and come up with a reason (cause you have one... don't you?

)
If they say no or why should I? say that you will "owe them one" and "would really appreciate it", half the time they will forget that you even said it
Of course I personally wouldn't ask someone to clean my garage LOL but there you go, thats my example