Graphs of the Other Trigonometric Functions · Challenge problem

The graph of $y=a\tan(bx+c)$, with $a>0$ and $b>0$, has adjacent vertical asymptotes at $x=\dfrac{\pi}{12}$ and $x=\dfrac{7\pi}{12}$, and passes through the point $\left(\dfrac{5\pi}{12},\,2\right)$. Find $a$.