Triangulating sound method works for a single target.
I doubt it would work if there are a number of mosquitoes in the room.
FFT it before triangulating, I'm sure mosquittoes are buzzing at fairly slowly drifting frequency (which you can lock into and track despite the drift), and each have a different frequency. This is the feeling I have trying to sleep despite mosquittoes: different pitch everywhere, can track every moment quite accurately with the human auditory system. Obviously this only works with fairly limited number of mosquittoes and requires a bit of luck so that they don't happen to fall within too close frequencies to begin with, but I would guesstimate this could work quite well up to maybe 5-10 simultaneous mosquittoes.
In any case, the range of such system would be limited (square law of amplitude), so you would use a distributed approach and use multiple such systems independently covering different areas. They could share information whenever a mosquitto is getting near to the end of the range of one system.
As a side note, before starting to automagically kill insects, make sure they are not the pollinating kind. For example, UV light attracts insects that are genetically programmed to go for flowers (with their UV signals), these insects are extremely important for the ecosystem and fairly beningn. The bad guys you want to get rid off are those who come for your blood, and these detect CO2, body temperature, and so on.
If all this sounds too easy, here's a true engineering challenge: before zapping the mosquitto with laser, figure out how to remotely test the flying mosquitto for malaria, and only zap it if positive.