I don't much like it, but you can still get rid of the cosine using .
Rearrange, Square, Rearrange, and notice that it factors a little, (sin(x)+1)(Other Stuff) = 0.
Irritatingly, sin(x) + 1 = 0 leads to (3/2)pi which is NOT a solution of the original expression. Your task is to find the remaining Real solution to the cubic expression in sin(x). I could tell you what it is, exactly, but you totally do NOT want to know that. Perhaps a numerical solution would be best. Start looking around x = 3.5