CONO-SUR 2008 Problem 2

Let $P$ be a point in the interior of triangle $ABC$ . Let $X$ , $Y$ , and $Z$ be points on sides $BC$ , $AC$ , and $AB$ respectively, such that $<PXC=<PYA=<PZB$ . Let $U$ , $V$ , and $W$ be points on sides $BC$ , $AC$ , and $AB$ , respectively, or on their extensions if necessary, with $X$ in between $B$ and $U$ , $Y$ in between $C$ and $V$ , and $Z$ in between $A$ and $W$ , such that $PU=2PX$ , $PV=2PY$ , and $PW=2PZ$ . If the area of triangle $XYZ$ is $1$ , find the area of triangle $UVW$ .