Step 1: Use the formula for pair of lines
For $ax^2+2hxy+by^2=0$, $\tan\theta = \frac{2\sqrt{h^2-ab}}{|a+b|}$. Here $a=2, 2h=7, b=3$.
Step 2: Compute
$h^2-ab = \frac{49}{4}-6 = \frac{25}{4}$, so $2\sqrt{h^2-ab} = 5$ and $a+b = 5$. Hence $\tan\theta = 1$.
Step 3: Evaluate
Divide numerator and denominator by $\cos\theta$: $\frac{2-3\tan\theta}{4\tan\theta+5} = \frac{2-3}{4+5} = -\frac19$. Option (C).
Final Answer:
-1/9.
\[ \boxed{\text{(C)}\ -\frac19} \]