In general, we have
[tex]\csc x=-1\implies\sin x=\dfrac1{-1}=-1\implies x=\dfrac{3\pi}2+2n\pi[/tex]
for integers [tex]n[/tex]. We get a solution in the interval [tex][3\pi,4\pi][/tex] for [tex]n=1[/tex], which gives
[tex]x=\dfrac{7\pi}2[/tex]
and so the answer is C.
