Looking again, I realize you did take the inverse sine; since you are working in radians, you got -0.10016742, which you then rounded to -0.1, so it looked as if you had not. (Your notation, with the vertical bar, is unfamiliar to me.)
On the other hand, you then made a mistake I didn't notice before (because I was only looking at the general ideas). The two possible angles are -0.10016742 and pi - (-0.10016742), which is 3.24176, not 3.04. Then you made some calculation error for the first solution, which I can't figure out. (You calculated correctly on the second, which was already wrong.)