The order of the letters is important. ADOC implies that A is on an extension of a diameter of the circle, (on the D side), and ABE implies that the point B lies between A and E.

The angle CAE is equal to the angle ACB, so choose to maximise this angle instead.

Start by picturing the construction for a small value of ACB and argue that the angle can be increased upto the limiting case when B and E come together and A(BE) is a tangent to the circle at BE.

(Beyond that, either B and E switch places or B moves back towards D, whichever way you choose to look at it.)

From there it's relatively easy to calculate the angle. It turns out to be thirty degrees.