$\begin{array}{l}
{u_1} = \cos \left( {\dfrac{{1.\pi }}{4}} \right) + {\sin ^2}\left( {\dfrac{{2.1\pi }}{3}} \right) = \dfrac{{3 + 2\sqrt 2 }}{4}\\
{u_2} = \cos \left( {\dfrac{{2.\pi }}{4}} \right) + {\sin ^2}\left( {\dfrac{{2.2\pi }}{3}} \right) = \dfrac{3}{4}\\
{u_3} = \cos \left( {\dfrac{{3.\pi }}{4}} \right) + {\sin ^2}\left( {\dfrac{{2.3\pi }}{3}} \right) = - \dfrac{{\sqrt 2 }}{2}\\
{u_4} = \cos \left( {\dfrac{{4.\pi }}{4}} \right) + {\sin ^2}\left( {\dfrac{{2.4\pi }}{3}} \right) = - \dfrac{1}{4}\\
{u_5} = \cos \left( {\dfrac{{5.\pi }}{4}} \right) + {\sin ^2}\left( {\dfrac{{2.5\pi }}{3}} \right) = \dfrac{{3 - 2\sqrt 2 }}{4}
\end{array}$
