[tex]\cos^2\theta=1-\sin^2\theta[/tex]
[tex]2\cos^2\theta=\sin\theta+1[/tex]
[tex]2-2\sin^2\theta=\sin\theta+1[/tex]
[tex]2\sin^2\theta+\sin\theta-1=0[/tex]
[tex](2\sin\theta-1)(\sin\theta+1)=0[/tex]
[tex]2\sin\theta-1=0\implies \sin\theta=\dfrac12\implies\theta=\dfrac\pi6,\dfrac{5\pi}6[/tex]
[tex]\sin\theta+1=0\implies\sin\theta=-1\implies\theta=\dfrac{3\pi}2[/tex]
