Find the value of $k$ if for the complex numbers $\;z_{1}\;$ and $\;z_{2}\;,|1-\overline{z_{1}}z_{2}|^{2} - |z_{1} - z_{2}|^{2}= k (1-|z_{1}|^{2}) (1-|z_{2}|^{2})$

Question

$(a)\;1\qquad(b)\;\pm6\qquad(c)\;\pm3\qquad(d)\;4$