Let $AB$ and $PQ$ be two vertical poles,$160 \ m$ apart from each other. Let $C$ be the middle point of $B$ and $Q$,which are the feet of these two poles. Let $\frac{\pi}{8}$ and $\theta$ be the angles of elevation from $C$ to $P$ and $A$,respectively. If the height of pole $PQ$ is twice the height of pole $AB$,then $\tan^{2} \theta$ is equal to

• A
  $\frac{3-2 \sqrt{2}}{2}$
• B
  $\frac{3+\sqrt{2}}{2}$
• C
  $\frac{3-2 \sqrt{2}}{4}$
• D
  $\frac{3-\sqrt{2}}{4}$