I was watching this video and noticed the title. I would have thought that it would be something like 自分の目で確かめよう to mean "see for yourself". But instead it is
その目で確かめよう
which would have the literal meaning of "Confirm with those eyes." その手 seems like it might be used in a similar way (その手に触れるまで seems like it might something similar and at least appears in some songs/movies), but when are some other times one might use そのX to mean "your X"?