Answer:
[tex]$\frac{3\pi }{2}$[/tex]
Step-by-step explanation:
Solve for the interval: [tex][0, 2\pi)[/tex]
[tex]4 \csc(\theta)+1=-3[/tex]
[tex]4 \csc(\theta)=-4[/tex]
[tex]\csc(\theta)=-1[/tex]
[tex]$\frac{1}{\sin(\theta)} =-1 \Rightarrow \sin(\theta)=-1$[/tex]
We have [tex]\sin(\theta)=-1[/tex] for coterminal angles [tex]$\frac{3\pi }{2}+2\pi n$[/tex]
Once we just want the interval [tex][0, 2\pi)[/tex]
The solution is [tex]$\frac{3\pi }{2}$[/tex]
