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To answer the question in more depth, your load current is 1.6mA. If the transistor has a gain of 100, then your base current will be 16uA. You need the current going through the Zener to be large in proportion to this. If it is not, the current in the base will steal from the current through the Zener and affect the voltage across the Zener. Standard Zeners need about 5mA flowing through them, which is high compared with 16uA, so rate your Zener resistor so that with a voltage drop across it of (Vin - Vz) you get 5mA.
Which bit of the opto are your powering? If it is the diode, you will need a series resistor between the output of the regulator and the diode as the diode will have a voltage drop across it of about 1.5V.