Answer
The solutions of the provided trigonometric equation are $\theta =\frac{\pi }{3},\frac{5\pi }{3},0$.
Work Step by Step
We have the equation as $2+\cos 2\theta =3\cos \theta $.
By solving the equation,
$\begin{align}
& 2+\cos 2\theta =3\cos \theta \\
& 2+2co{{s}^{2}}\theta -1=3\cos \theta \\
& 2{{\cos }^{2}}\theta -3\cos \theta +1=0
\end{align}$
Then,
$\begin{align}
& 2{{\cos }^{2}}\theta -2\cos \theta -\cos \theta +1=0 \\
& \left( 2\cos \theta -1 \right)(\cos \theta -1)=0 \\
& \cos \theta =\frac{1}{2},1
\end{align}$
Hence, in the provided range, we get, $\theta =\frac{\pi }{3},\frac{5\pi }{3},0$
