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 $UVW$.