An Azumaya Algebra Version of the Kneser–Tits Problem for Groups of TypeD4

We solve the following problem related to the Kneser–Tits conjecture, for Azumaya algebras. Given an Azumaya algebra D of rank 4 that is not a division algebra, whose center K is three-dimensional over the ground field F, such that cor K/F D is trivial, is it true that every element of D having reduced norm in F is a product of n elements having both reduced norm and reduced trace in F? This is true for n ≥ 3, but false for n = 2.