Answer
$\cos \theta =\dfrac {\pi }{3}+2\pi k$
Work Step by Step
$2\cos ^{2}\theta -7\cos \theta +3=0$
$\Rightarrow \cos \theta =\dfrac {7\pm \sqrt {7^{2}-4\times 2\times 3}}{2\times 2}=\dfrac {7\pm 5}{4}=3;\dfrac {1}{2}$
$cos \theta $ cannot be greater than 1 so $\cos \theta =\dfrac {1}{2}\Rightarrow \theta =\cos ^{-1}\left( \dfrac {1}{2}\right) =\dfrac {\pi }{3}+2\pi k$
