Factor out [tex]\cos\theta[/tex]:
[tex]\cos\theta\csc\theta-2\cos\theta=\cos\theta(\csc\theta-2)=\cos\theta\left(\dfrac1{\sin\theta}-2\right)=0[/tex]
Then either
[tex]\cos\theta=0\implies\theta=\dfrac\pi2+n\pi[/tex]
or
[tex]\dfrac1{\sin\theta}-2=0\implies\sin\theta=\dfrac12\implies\theta=\dfrac\pi6+2n\pi\text{ or }\theta=\dfrac{5\pi}6+2n\pi[/tex]
where [tex]n[/tex] is any integer.
