FIR filter (from zeros to filter coefficients)
First of all a discrete filter having a zero somewhere means it's Z-transform (which is a polynomial) acquires the value 0 there.

If you remember, there is a theorem in calculus saying: for a polynomial to have real coefficients any complex roots which are not on the real line must come in complex conjugate pairs. So if $z_0 = e^{j\omega /6}$ then $z_1 = e^{-j\omega / 6}$ and that gives : $$(z - z_0)(z - z_1)C = (z - e^{j\omega /6})(z - e^{-j\omega /6})C$$

Then to find the constant $C$ solve the equation with the absolute value of the polynomial equals 1 for $z = e^{j\pi}$.