Prove that

As we know that,

$\cos 60^{\circ}=\frac{\sqrt{3}}{2}$

Thus,

if $2 \cos 3 \theta=1$

$\Rightarrow \cos 3 \theta=\frac{1}{2}$

$\Rightarrow 3 \theta=60^{\circ}$

$\Rightarrow \theta=20^{\circ}$

Hence, the correct option is (c).