已知 $\theta \in\left(\frac{3 \pi}{4}, \pi\right), \tan 2 \theta=-4 \tan \left(\theta+\frac{\pi}{4}\right)$, 则 $\frac{1+\sin 2 \theta}{2 \cos ^2 \theta+\sin 2 \theta}=$
$\text{A.}$ $\frac{1}{4}$
$\text{B.}$ $\frac{3}{4}$
$\text{C.}$ 1
$\text{D.}$ $\frac{3}{2}$