I'm planning on recording a music video and I want to have 3 different angles shown throughout. This will involve recording the song 3 times, which is not a problem.

My question is how will I be able to effectively link together my 3 different angles into a single video, whilst not interfering with the audio flow of the song? I'm using Windows Movie Maker, and it has the trimming feature, but will this be accurate enough to keep the transitions between angles smooth?

For example, I don't want to have shown 10 seconds of angle A, then switch to angle B to find that it does not begin exactly where A ended, hence disrupting the smoothness of audio transition.

One would assume the band will be mixing the sound through a sound board. Most sound boards have different outputs including stereo.

You will be better off with controlled sound instead of raw sound from the camera microphone plus the sound will be different when in a different place so for best result a separate and mixed and controlled soundtrack is preferred.

Are you really limited to only one camera. Twould be much better to just use three (better would be four or five or six).

Putting the multiple camera versions together after the music stops is called editing or post production.

Some software will let you open all video tracks at one time in the program's workspace or timeline and sync them all up via timecode and then let you choose which camera angles you want to show by setting cut in and out points and then when all of your cut or edit points (and transitions and effects) are programmed then you just tell the program to finish or "render" your program.
OR
You can do what I have done many times - it just takes practice.
Pick one video track and put it in the main timeline of a less complicated editing program like ULead Video Studio.
Then drop in your audio track into the audio timeline and manually sync it to the base video track.
Then go through the other camera versions and pick scenes from them for insertion within the main track.

I have actually mixed six camera versions of three one hour sets manually in this manner syncing all to a separately mixed soundtrack and I did the picture sync to the sound for each "cut" my just tapping my feet and clicking in/out points with a mouse button.

You will be better off with multiple cameras capturing the song all at the same time then later edited together synced to the soundtrack.
Tha's about as short an overview as I can create.
EDITED TO ADD - personal preference - quit trying to use the Microsoft program. There are a number of not too expensive and much better consumer editing programs - most have free trial versions available via online download. IMO - all will make you job A LOT EASIER than movie maker.
goodluck - editing - even simple manually sync to sound - is a lot of fun!

Thanks for your advice.

This is going to be a pretty low budget production, so no sound board. Also, I only have 2 available cameras.

Can you give me examples of this software? I definitely think this would be more time-efficient than the other method (the ULead one).

Again, thanks for your help!