See if you can hear the washer fluid pump working from outside the car, but DO NOT raise the hood while testing this. On some cars, running the windshield wipers while the hood is raised will cause contact with the hood and wipers, resulting in paint damage to the hood. I don't know if this is the case with the Mazda3 (what year do you have, btw?).
Anyway, see if you can hear the pump working. If you can't hear anything, the pump may be busted. Otherwise, I'd suggest cleaning the nozzles with a pin, and if that doesn't work, try cleaning the nozzle with CLR (but be careful as CLR shouldn't be used on plastics or painted surfaces).