Step-by-step explanation:
Recall that
[tex]\cos{2\theta} = 1 -2\sin^2\theta[/tex]
so we can write our original equation as
[tex]3 - 6\sin^2{\theta} + \sin{\theta} = 1[/tex] or
[tex]6\sin^2{\theta} - \sin{\theta} - 2 =0[/tex]
Let [tex]x = \sin{\theta}[/tex] so our equation becomes
[tex]6x^2 - x - 2= 0[/tex]
which gives us two roots: [tex]x = -\frac{1}{2}[/tex] and [tex]x = \frac{2}{3}[/tex].
This is equivalent to [tex]\theta = 150°[/tex] and [tex]\theta = 41.8°[/tex]
