DEB is a chord of a circle such that DE=3 and EB=5. Let O be the center of the circle. Join OE and extend OE to cut the circle at C. If CE=1 then what is tan(OEB)?
Use the intersecting chords theorem to calculate the radius of the circle.
(Extend CO to meet the circle again at A, then AE.EC = BE.ED .)
That gets you the dimensions of the triangle BOE and you can then use the cosine rule to calculate the angles.