2.45: Tangent to a trigonometric curve and intercept distance

Find the equation of the tangent to the curve $2y = \tan 2x + 7$ at the point where $x = \dfrac{\pi}{8}$. Give your answer in the form $ax - y = \dfrac{\pi}{b} + c$, where $a$, $b$ and $c$ are integers.

This tangent intersects the $x$-axis at $P$ and the $y$-axis at $Q$. Find the length of $PQ$.