Let $x, y$ and $z$ be distinct elements of the set $\left\{\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}\right\}$ such that
$$\sin x < \tan y < \sec z$$
Which of the following is the correct ordering of $x$, $y$ and $z$?
A) $x < y < z$
B) $y < x < z$
C) $y < z < x$
D) $z < x < y$
E) $z < y < x$