How to use a phototriac coupler to trigger the main triac?
It's for on/off control only. After the opto-coupler sees the LED going on it waits for the next zero-crossing of the mains voltage, at which point it switches on. After switching off, like any triac it remains on until the current goes below a hold-value. The circuit doesn't need to tell te microcontroller; it takes care of it all by itself.
Opto-couplers with zero-crossing switch are useful for switching resistive loads, like incandescent bulbs. They don't offer advantages for switching reactive loads.  

Note that with typical PCB pads there may be not sufficient creepage distance between the pins on the control side (1, 2) and the load side (4, 5, 6). In Europe this should be 6 mm. The NVZ version may offer a solution.  

The PC3SD21NTZ sounds like a somewhat exotic part. If you need more of them, you may consider the compatible MOC3031/3041 (3031 for 115 V, 3041 for 230 V).