A 3-inch gun adds depth rather than duplicating a missile

Why add 3-inch guns when a Type 45 already has a 4.5-inch gun and surface-to-air missiles?

Additional guns create another magazine and field-of-fire layer between missiles and close-in weapons, increasing the volume available against leakers and saturation attacks.

The 4.5-inch gun had a general-purpose and fire-support role, while several smaller mounts could be placed around the superstructure. Multiple 3-inch guns could cover different arcs and contribute separate magazines after long- and short-range missile layers had engaged. Close-in weapons would then remain as the final defensive step. The arrangement resembles wartime cruisers carrying 6-inch, 4-inch, and 40 mm weapons rather than expecting one calibre to do every job. The point is redundancy and sustained volume of fire, not adding a second weapon merely because it is available.