Dear Hellbent,

Sorry I did'nt help you when I first saw your thread. And that must be the reason for you to send me a privet message. That is because I just came home after a tiresome days work and I did'nt have that feeling to answer threads.

Anyway now do you know your mistake,

When, $\displaystyle Sin\theta=\frac{2}{3}$

$\displaystyle \theta=arcsin\frac{2}{3}$ gives all the solutions that could be taken for $\displaystyle \theta$. When writing the general solution you must take $\displaystyle \theta $ such that it is in the first quadrant. That is why I used $\displaystyle Sin^{-1}\frac{2}{3}$. If this seems a bit confusing please refer,

General Solutions of Trigonometric Functions, Maths First, Institute of Fundamental Sciences, Massey University
Hope this will help you.