Answer
.92
Work Step by Step
We solve the equation using the properties of trigonometric functions. Note, there is a general solution since trigonometric identities go up and down and this can pass through a given value of y many times. Solving this, we find:
$$\csc \left(x^2\right)=\frac{4}{3} \\ x^2=arccsc \left(\frac{4}{3}\right) \\ x=.92$$