Tangential acceleration in circular motion

We know that the magnitude of tangential component of acceleration is,
a_tangential = dv/dt (where v is speed)
So clearly a_tan = 0 for uniform circular motion (as v is constant)

But what about non-uniform circular motion?
I can see a_tan = 0 only when v = constant. But in non uniform circular motion v is not constant.
Does it mean that a_tan can never be zero if the particle is moving in non-uniform circular motion?
(It never seems to be the case.)
Would someone please explain?