2008 worldcon site selection|
You have led me to think about the word "ept." Apparently "inept" is, etymologically, a trivial variation on "inapt," and so the opposite would be "apt." However, a more appropriate, and still related, opposite would be "adept" (for those occasions when you feel compelled to use a word that's in the dictionary).
The root of "inept" and "apt" is latin for "to fasten," while the root of "adept" is latin for "to grasp." So both of them have a connotation of having a hold on things, having it together, being able to find your ass with both your hands, etc.