Step 1: Use the difference of cosines:
$\cos4\theta-\cos3\theta=-2\sin\dfrac{7\theta}{2}\sin\dfrac{\theta}{2}=0$.
Step 2: Solve each factor:
$\sin\dfrac{7\theta}{2}=0$ gives $\theta=\dfrac{2n\pi}{7}$. $\sin\dfrac{\theta}{2}=0$ gives $\theta=2n\pi$, which is included in the first family.
Step 3: Pick:
$\theta=\dfrac{2n\pi}{7}$, option A.
Final Answer:
The factor sin(7 theta / 2) gives theta = 2n pi / 7.
\[ \boxed{\text{(A) }\dfrac{2n\pi}{7},\ n\in Z} \]