[tex]\bf csc(\theta)=\cfrac{1}{sin(\theta)}\\\\
-----------------------------\\\\
6sin(\theta)-3csc(\theta)=0\implies 6sin(\theta)-3\cfrac{1}{sin(\theta)}=0
\\\\\\
6sin(\theta)-\cfrac{3}{sin(\theta)}=0\impliedby \textit{multiplying both sides by }sin(\theta)
\\\\\\[/tex]
[tex]\bf 6sin^2(\theta)-3=0\implies 6sin^2(\theta)=3\implies sin^2(\theta)=\cfrac{3}{6}
\\\\\\
sin(\theta)=\sqrt{\cfrac{1}{2}}\implies sin^{-1}[sin(\theta)]=sin^{-1}\left( \cfrac{1}{\sqrt{2}}\right)
\\\\\\
\measuredangle \theta=sin^{-1}\left( \cfrac{1}{\sqrt{2}}\right)\implies \measuredangle \theta=sin^{-1}\left( \cfrac{\sqrt{2}}{2}\right)[/tex]
now, if you check your Unit Circle, that's a well known angle for the 1st and 2nd quadrants
