If in a $\Delta$ le $ABC,A=\large\frac{\pi}{4}$ and $\tan B\tan C=\alpha$ then the value of $\alpha$ lies in

Question

$\begin{array}{1 1}(a)\;(-\infty,3-2\sqrt 2)\\(b)\;(3-2\sqrt 2,3+2\sqrt 2)\\(c)\;(-\infty,3-2\sqrt 2)\cup (3+2\sqrt 2,\infty)\\(d)\;None\;of\;the\;above\end{array}$