Trigonometric Functions · Superchallenge problem

Let $P=(\cos\theta,\sin\theta)$ with $0<\theta<\dfrac{\pi}{2}$. The line tangent to the unit circle at $P$ meets the $x$-axis at $A$ and the $y$-axis at $B$, and $O$ is the origin. If the perimeter of triangle $OAB$ is $6$, find $\sin2\theta$.