Given equation has more than two roots if it is an identity
$\Rightarrow \cos 3\theta +1=0; \mathrm{}2\cos 2\theta -1=\mathrm{0 }\mathrm{}\mathrm{}\mathrm{a}\mathrm{n}\mathrm{d }\mathrm{}\mathrm{}1-2\cos \theta =0$
$\Rightarrow \cos 3\theta =-1\mathrm{}\mathrm{}\mathrm{}\Rightarrow \theta =\pm \frac{\pi }{3}$ which does not satisfy $2\cos 2\theta -1=0$

Hence, no value possible