$$ \left|\psi\right> = \cos{\left(\frac{\theta}{2}\right)}\left|0\right> + e^{i\phi}\sin{\left(\frac{\theta}{2}\right)}\left|1\right> $$

$$ \left|\psi\right> = \cos{\left(\frac{\theta_0}{2}\right)}\left|00\right> + e^{i\phi_0}\sin{\left(\frac{\theta_0}{2}\right)}\cos{\left(\frac{\theta_1}{2}\right)}\left|01\right> + e^{i\phi_1}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\cos{\left(\frac{\theta_2}{2}\right)}\left|10\right> + e^{i\phi_2}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\sin{\left(\frac{\theta_2}{2}\right)}\left|11\right> $$

$$ \left|\psi\right> = \cos{\left(\frac{\theta_0}{2}\right)}\left|000\right> + e^{i\phi_0}\sin{\left(\frac{\theta_0}{2}\right)}\cos{\left(\frac{\theta_1}{2}\right)}\left|001\right> + e^{i\phi_1}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\cos{\left(\frac{\theta_2}{2}\right)}\left|010\right> + e^{i\phi_2}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\sin{\left(\frac{\theta_2}{2}\right)}\cos{\left(\frac{\theta_3}{2}\right)}\left|011\right> + e^{i\phi_3}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\sin{\left(\frac{\theta_2}{2}\right)}\sin{\left(\frac{\theta_3}{2}\right)}\cos{\left(\frac{\theta_4}{2}\right)}\left|100\right> + e^{i\phi_4}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\sin{\left(\frac{\theta_2}{2}\right)}\sin{\left(\frac{\theta_3}{2}\right)}\sin{\left(\frac{\theta_4}{2}\right)}\cos{\left(\frac{\theta_5}{2}\right)}\left|101\right> + e^{i\phi_5}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\sin{\left(\frac{\theta_2}{2}\right)}\sin{\left(\frac{\theta_3}{2}\right)}\sin{\left(\frac{\theta_4}{2}\right)}\sin{\left(\frac{\theta_5}{2}\right)}\cos{\left(\frac{\theta_6}{2}\right)}\left|110\right> + e^{i\phi_6}\sin{\left(\frac{\theta_0}{2}\right)}\sin{\left(\frac{\theta_1}{2}\right)}\sin{\left(\frac{\theta_2}{2}\right)}\sin{\left(\frac{\theta_3}{2}\right)}\sin{\left(\frac{\theta_4}{2}\right)}\sin{\left(\frac{\theta_5}{2}\right)}\sin{\left(\frac{\theta_6}{2}\right)}\left|111\right> $$

$$ \left( {\begin{array}{ccc} \cos{\phi_i} & -\sin{\phi_i} & 0 \\\ \sin{\phi_i} & \cos{\phi_i} & 0 \\\ 0 & 0 & 1 \\\ \end{array} } \right) \left( {\begin{array}{ccc} \cos{\theta_i} & 0 & \sin{\theta_i}\\\ 0 & 1 & 0 \\\ -\sin{\theta_i} & 0 & \cos{\theta_i}\\\ \end{array} } \right)\left( {\begin{array}{c} 0 \\\ 0 \\\ 1 \\\ \end{array} } \right) $$