EDIT: Does your book also give x=0 as a solution?

As you have written it you are right but the book's answer suggest your limits are actually . This means are allowable

You are cancelling out sin(x) in the second step which is potentially equal to 0. Instead, solve this equation via factorising.

Either: (which is where -180,0,180 comes from)

or which you did

It is also interesting to note that this equation has a vertical asymptote at