No you don't. You need 70% attack speed on gear which doesn't require epiphany. Even if you go over 60% cap without Epiphany, as long as your gear has 75% attack speed, the bonus will activate. 60% of the 75% attack speed will be counted but the 15% afterwards isn't counted.
But if you want to feel the 75% attack speed along with the 70% bonus, then you can use Epiphany (5) to really have a feel for it.