Answer
$\theta =\dfrac {\pi }{4}+2\pi k;$
$ \theta=\dfrac {7\pi }{4}+2\pi k$
Work Step by Step
$sec\theta \left( 2\cos \theta -\sqrt {2}\right) =0\Rightarrow \dfrac {\left( 2\cos \theta -\sqrt {2}\right) }{\cos \theta }=0\Rightarrow 2\cos \theta =\sqrt {2}\Rightarrow \theta =\cos ^{-1}\dfrac {\sqrt {2}}{2}=\dfrac {\pi }{4}+2\pi k;\dfrac {7\pi }{4}+2\pi k$
