[tex]\bf sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-----------------------------\\\\
3\sqrt{2}sec(\theta)+7=1\implies 3\sqrt{2}sec(\theta)=-6\implies sec(\theta)=\cfrac{-6}{3\sqrt{2}}\\\\
-----------------------------\\\\
now\qquad -\cfrac{6}{3\sqrt{2}}\implies -\cfrac{2}{\sqrt{2}}\implies -\cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies -\cfrac{2\sqrt{2}}{2}\implies -\sqrt{2}\\\\[/tex]
[tex]\bf -----------------------------\\\\
\cfrac{1}{cos(\theta)}=-\sqrt{2}\implies \cfrac{1}{-\sqrt{2}}=cos(\theta)\\\\
-----------------------------\\\\
now\quad -\cfrac{1}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies -\cfrac{\sqrt{2}}{2}\\\\
-----------------------------\\\\
-\cfrac{\sqrt{2}}{2}=cos(\theta)\implies \theta=
\begin{cases}
\frac{3\pi }{4}\\\\
\frac{5\pi }{4}
\end{cases}[/tex]
