If I got entangled in monofilament, I'd try to identify where I was caught and cut the line. I'd also immediately signal my buddy and indicate my plight. If I were separated from my buddy (in which case, shame on me AND him), this is one of the few times when removing one's gear underwater might be necessary. Luckily, since I don't dive weight integrated, I could do that without too much hardship.
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A couple of thoughts:
If you didn't see the monofillament, perhaps your buddy didn't either and you are both entangled.
I think about this a lot, for some reason. I always think that removing your gear is a viable option. I do carry shears but only one pair.
I have actually removed my BC (weight intergrated) in order to re-secure the tank to the BC because my buddy (a new diver) was unable to secure it. It was a bit of a rodeo because I didn't think about the weights being in the BC and not on me before I tried it, but I managed it. I was aware that I was only in 40' of water and could easily do a CESA if need be. Also, I wear a dive skin, not a wet suit so my bouyancy wasn't as much as it would have been otherwise.
Now I have a BP and don't carry extra weight on me, so if the situation arose, I'd be in the same boat as with a w/i BC. And removing the BP/W is more cumbersome than the BC in that you have the crotch strap (which is one more place to get entangled if you remove your equipment). Hmmm. I guess I have to rethink this now with the new equipment.