In addition to what S.S.Guy mentioned, is that the gate transformer, must be able to support the required primary volt-second product without saturation.
For powerline gate drive, usually you will require as much volt-seconds as possible, since the Triacs take some time to latch.
For instance, Coilcraft's SD250-3L is capable of withstanding 375 V-usec, which translates to about 125 microseconds at 3 volt of applied primary voltage (I'm considering 0.3 volt parasitic voltage drop at the primary).
If your microcontroller can reliably ensure that this pulse width value is not exceeded, then the transformer will not saturate and the current limiting resistor R1 is not required.
If the transformer is too large, there is an alternative: use a smaller device with lower volt-seconds, and use picket-fence triggering. Which is a fancy way of saying a closely spaced burst of narrower pulses.
I've used this last method to trigger Triacs succesfully since the days of unijunction transistors (back in the mid 1970s).