Looking for and SMD optocoupled TRIAC
The 1.5V you mention is the voltage drop across the opto-coupler's LED, and this is fairly constant. You can't just apply 3.3V because a way too high current will flow, which may destroy the LED. In this case the current will be limited by the Arduino, but you have to limit it to a lower level. The MOC3023 only needs 5mA maximum to operate the triac, and has an AMR (Absolute Maximum Rating) of 60mA. (Note: you're not supposed to operate a device continuously at AMR!).
Let's pick a safe value: 10mA. \$V_F\$ is typically 1.15V, then we can calculate the series resistor we'll need to set the current to 10mA:  


  \$ R = \dfrac{\Delta V}{I} = \dfrac{3.3V - 1.15V}{10mA} = 215\Omega \$  


We pick the closest E12 value, 220\$\Omega\$. But wait, that's for the typical \$V_F\$, the datasheet says it can be as high as 1.5V. What will the current then be?  


  \$ I = \dfrac{\Delta V}{R} = \dfrac{3.3V - 1.5V}{220\Omega} = 8.2mA \$ 


So that's still enough to trigger the triac, and well within the limits of what the Arduino can deliver.