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If the video you made is for teaching purposes only (not for commercial purposes) and you are only using the theme music for background (and not the whole piece), you may be able to use under the "Fair Use" doctrine of Copyright law.
However, if your video will be used for commercial purposes or to make a profit, then you will need to obtain the permission of the copyright owner. In order to figure out the copyright owner, you will need to contact the movie studio who released the movie as a starting point and they will point you in the right direction. If the use is for profit, they may also charge you for using their work.
More on Fair Use: http://www.royaltyfreemusic.com/public-domain/consideration-fair-use.html
This has been of great assistance and has helped me to make an informed decision.