How to find voltage on zener diode while there is a current source
There are only two options here the zener is ether conducting or it isn't

If it is:

$$\dfrac{Vo-Vz}{R1}+\dfrac{Vo-Vd}{R2}+\dfrac{Vo-Vd}{R3} = I1$$

If it isn't: 

$$\dfrac{Vo-Vd}{R2}+\dfrac{Vo-Vd}{R3} = I1$$

Where Vo is the voltage a junction of the diodes, Vz is the zener voltage and Vd is forward diode drop (0.6V).

What do these say?  Does only one make sense?