Cscθ=-2.1625
\(csc(x)=-2.1625\\ \frac{1}{sin(x)}=-2.1625\\ \frac{1}{-2.1625}=sin(x)\\ sin(x)=\frac{1}{-2.1625}\\ x=asin(\frac{1}{-2.1625})\\\)
asin(-1/2.1625) = -27.543876784605 degrees
\(x\approx 180+27.5+360n \qquad x=360-27.5+360n\qquad n\in Z\\ x\approx 107.5+360n \qquad or \qquad \;x\approx332.5+360n\qquad \qquad n\in Z\\\)