how to exactly get an explicit form of a trig differential problem?

Question

I attempting to get an explicit form of a trigonometric function in terms of y and x. this is the problem and solution:

problem and solution image

i only got to the expression $\frac{1}{7}\ \sin(7y)\ = \ 7\cos^2\ (x)$ but I do not know how to express this explicitly, as a function y in terms of x.

thanks