I've done the scotch tape thing a lot of times long, long ago. Assuming the tape just broke:
1 Lay scotch tape sticky side up on a table or something. Tape it down at each end if you need. You only need a short stretch of sticky side visible.
2 Straighten out the cassette tape. If you don't get all the twists out you will have turns in it and it won't play right. Reel most all of it back into the tape so that you only have maybe 6 inches of slack.
3 Lay the first half with the outward-facing surface UP, so that the one torn end is about half way across the sticky tape. Press it down so it's adhered.
4 Lay the second half the same way with that end butted against the first end. Press it down also.
5 Use sharp scissors or a razor blade to cut the excess tape off both sides, leaving only the scotch tape directly under the magnetic tape.
6 Reel it in and you're done. It will probably click when it goes past that part.
NOW - record it again onto something else (MP3 file, whatever), so when it breaks again you will still have it.