I think Standard CT and (one of the cuts of) Gothic 725 are the closest digital matches to 'Stadtheater'. Maybe the a's foot was cut off in the Stadtheater poster?
Royal Grotesk and AG Old Face could be on that list too, but the bowl of the a and its stem join in a sharp corner. Josef Müller Brockmann used Akzidenz Grotesk in many (most?) of his works. This post on Fonts In Use has a Brockmann poster with an 'a' like the example above. The font is ID'ed as Akzidenz Grotesk.