Anti-aircraft armament for a 28,000-ton fast battlecruiser

How much anti-aircraft armament could a 28,000-ton, six-15-inch-gun fast battlecruiser carry?

A useful battery, particularly if the design focused on twin 4.5-inch dual-purpose guns.

The answer relies on disciplined secondary-battery design rather than many different weapon types. Concentrating on 4.5-inch dual-purpose guns preserves useful anti-surface and anti-aircraft fire while controlling weight and internal complexity.