

Open the video in MPEG Streamclip. Choose to export your video in the desired format (Quicktime Movie, AVI, etc.) You will see near the bottom of the exporter menu that there is a "crop" checkbox and spaces to fill in the amount you want cropped off of top, bottom or sides of a video.

If your fan video in the 4:3 (fullscreen) aspect ratio (but with letterbox bars, because the video itself is in the 16:9 "letterbox" aspect ratio), then it might have the pixel dimensions of 640x480—a common frame dimension for 4:3. But you know that the 16:9 aspect ratio should be 640x360. There are 120 extra pixels (480 - 360 = 120 ) that make up this black bar. So, you fill in the numbers "60" (half of 120) in the boxes next to "top" and 'bottom" in MPEG Streamclip, and it will crop the black bars off of your video!
This may take some guessing on your part if your video is some other frame dimension. If you are not sure how many pixels to crop, simply begin experimenting with different numbers, start to export the video, and see if the "Preview" pane shows that the black bars are completely cropped. You don't have to wait for the entire video to encode each time you try a new set of numbers. Just wait long enough to see if the black bars are removed. (But no need to overcrop!)
Leave the "scale" box (circled in lime green) unchecked. If you check it, it will squish your video, messing up its aspect ratio. The "scale" box can be useful on special occasions, however.