If \[{{z}_{1}},{{z}_{2}}\] are two complex numbers such that \[\left| \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}} \right|=1\] and \[i{{z}_{1}}=k{{z}_{2}}\], where \[k\in R\], then the angle between \[{{z}_{1}}-{{z}_{2}}\] and \[{{z}_{1}}+{{z}_{2}}\] is

• A. \[{{\tan }^{-1}}\left( \frac{2k}{{{k}^{2}}+1} \right)\]
• B. \[{{\tan }^{-1}}\left( \frac{2k}{1-{{k}^{2}}} \right)\]
• C. - \[2{{\tan }^{-1}}k\]
• D. \[2{{\tan }^{-1}}k\]