If $2\sec 2\mathrm{\theta }=\tan \mathrm{\varphi }+\cot \mathrm{\varphi }$, then one of the values of $\mathrm{\theta }+\mathrm{\varphi }$ is

$\begin{array}{l}2\sec 2\mathrm{\theta }=\tan \mathrm{\varphi }+\cot \mathrm{\varphi }\\ \text{ or }\frac{2}{\cos 2\mathrm{\theta }}=\frac{{\sin }^2\mathrm{\varphi }+{\cos }^2\mathrm{\varphi }}{\sin \mathrm{\varphi cos}\mathrm{\varphi }}\\ \text{ or }\frac{2}{\cos 2\mathrm{\theta }}=\frac{1}{\sin \mathrm{\varphi cos}\mathrm{\varphi }}\\ \text{ or }\cos 2\mathrm{\theta }=\sin 2\mathrm{\varphi }\\ \text{ or }2\mathrm{\theta }={90}^{\circ }-2\mathrm{\varphi }\\ \text{ or }\mathrm{\theta }+\mathrm{\varphi }=\frac{\mathrm{\pi }}{4}\end{array}$