I have done it with a thin strip of Sellotape - probably not the wisest thing to do!!
Nevertheless, it worked.........This Is What I Did.
Make sure that it is good tape and not 'corner/cheap shop' sticky tape or old tape. I say this because the glue used can sometimes leach out of the edges of the join and leave the rest of the video tape all gummed up.
I take it that both ends of the tape are out of the cassette?
If not then you will have to very carefully unscrew the caseing screws.
Watch that the tape is not twisted and that it goes over the guides etc in the right places.
You may need to refer to an undamaged tape to check this.
Cut a small thin-ish strip of Sellotape and lay it on the table vertically sticky side up (!).
Place the two broken tape edges onto the Sellotape horizontally together and then fold the top of the Sellotape down over the tape.
Press firmly.
I then trimmed the excess Sellotape with scissors to form a nice clean mend.
Not a professional job but it worked and is still working to this day.
I do the same to broken Audio Tapes too.
S.J.D.
September 2005