[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
-------------------------------\\\\
2cos^2(\theta )=sin(\theta )+1\implies 2[1-sin^2(\theta)]=sin(\theta )+1
\\\\\\
2-2sin^2(\theta )=sin(\theta )+1\implies 0=2sin^2(\theta )+sin(\theta )-1
\\\\\\\
0=[2sin(\theta )-1][sin(\theta )+1]\\\\
-------------------------------[/tex]
[tex]\bf 0=2sin(\theta )-1\implies 1=2sin(\theta )\implies \cfrac{1}{2}=sin(\theta )\implies \measuredangle \theta =
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}
\end{cases}\\\\
-------------------------------\\\\
0=sin(\theta )+1\implies -1=sin(\theta )\implies \measuredangle \theta =\frac{3\pi }{2}[/tex]
