Those making comments about flushing out a BCD with water have obviously never had to maintain a CCR.
Identification of bacteria in scuba divers' rinse tanks. - PubMed - NCBI
Alert Diver | Microbial Hazards
Emergency Breathing from Your BCD: Undercurrent 06/2011
DAN | Medical Frequently Asked Questions
Yes, it's a possibility you can use to possibly save your life, but you'd want to seek medical care/treatment directly afterwards.
To preserve gas, as others have said, the key is to relax. That's hard if you're otherwise stressed in a low-gas entanglement scenario.
Focus on stress management and keep your breathing as normal as possible. Mental discipline is the key here. Individuals have varying degrees of natural stress management, but it can be improved through realistic practice and decent training.
I wouldn't focus too much on 'fancy' breathing methods. The issue isn't about stretching your gas supply, but rather, it's about not accelerating your consumption.
That assumes, of course, that you had maintained a reasonable reserve when the (entanglement) problem arose.
I teach technical decompression and wreck penetration diving... and stress management is an important (pass/fail) part of this.
"Gas is time - time is life".
The last thing you'd want to do, if access to the surface is in any way impeded, is accelerate your gas consumption.
You have gas... because you've maintained a healthy reserve. If very wise, you'd also have a redundant supply. Knowing you have gas/time to deal with a problem is the biggest element in your stress management arsenal.
Take a deep breath, keep calm... and methodically extract yourself from the entanglement.
It also helps if you have confidence in your cutting device (is it even sharpened?) and have practiced and rehearsed for the scenario previously.
Entanglement drills are included in higher level overhead environment training. If you can predict or foresee that a specific problem might occur, then it's your responsibility to plan for it.. and mitigate that risk.