I know nothing about using tangents...but I have 2 other tricks up my sleeve that you can try:

1) Keyframe 2 frames in a row; the first frame being the LAST frame of the FIRST "scene," the second being the FIRST frame of the SECOND "scene." A rather makeshift 'cut'...

Pros/Cons:

+ This involves using only one camera, and is therefore simple to do

- Not exactly certain if this is safe to do this with just one camera...



2) Set up separate cameras to render the different "scenes."

Pros/Cons:

+ Absolutely certain that what could potentially go wrong as above CAN NOT happen with this

- More work

- More cameras to manage

- More renders to do (but, essentially, the same total render time)

- Having to piece the seperate scenes back together in some video-altering program like After Effects



Or you can wait until someone that has knowledge about tangents is able to help you out...but I hope I helped ^.^

Happy Rendering