Let $\mathrm{S}=\{\mathrm{\theta }\in (0,2\mathrm{\pi }):2\sin \mathrm{\theta }(4\sin \mathrm{\theta }-\sin 3\mathrm{\theta })=3\}$then which of the following statements is/are TRUE

$2\sin \mathrm{\theta }(4\sin \mathrm{\theta }-\sin 3\mathrm{\theta })=3$
$2\sin \mathrm{\theta }(4\sin \mathrm{\theta }-3\mathrm{sin\theta }+4 {\sin }^3\theta )=3$
$\begin{array}{l}\sin \mathrm{\theta }\left(\sin \mathrm{\theta }+4{\sin }^3\mathrm{\theta }\right)=\frac{3}{2}\Rightarrow 4{\sin }^4\theta +{\sin }^2\theta +\frac{1}{16}=\frac{3}{2}+\frac{1}{16}\\ {\left(2{\sin }^2\mathrm{\theta }+\frac{1}{4}\right)}^2=\frac{25}{16}\Rightarrow {\sin }^2\mathrm{\theta }=\frac{1}{2}\mathrm{\theta }\in (0,2\mathrm{\pi })\\ \Rightarrow \mathrm{\theta }=\frac{\mathrm{\pi }}{4},\frac{3\mathrm{\pi }}{4},\frac{5\mathrm{\pi }}{4},\frac{7\mathrm{\pi }}{4}\end{array}$