In which of the following sets the inequality ${\sin }^6\mathrm{x}+{\cos }^6\mathrm{x}>5/8$ holds good?

${\left({\sin }^2\mathrm{x}+{\cos }^2\mathrm{x}\right)}^3-3{\sin }^2{\mathrm{xcos}}^2\mathrm{x}\left({\sin }^2\mathrm{x}+{\cos }^2\mathrm{x}\right)>\frac{5}{8}$

$\begin{array}{l}\mathrm{or} 1-3{\sin }^2{\mathrm{xcos}}^2\mathrm{x}>\frac{5}{8}\\ \mathrm{or} \frac{3}{8}>3{\sin }^2{\mathrm{xcos}}^2\mathrm{x}\end{array}$

$\begin{array}{l}\Rightarrow 1-2{\sin }^{2}2\mathrm{x}>0\\ \Rightarrow \cos 4\mathrm{x}>0\\ \Rightarrow 4\mathrm{x}\in \left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)\\ \Rightarrow 4\mathrm{x}\in \left(2\mathrm{n\pi }-\frac{\mathrm{\pi }}{2},2\mathrm{n\pi }+\frac{\mathrm{\pi }}{2}\right),\end{array}$

          $\mathrm{n}\in \mathrm{Z}$, generalizing now verify.