Trots race had first radio broadcast, missing hectic finish (9)

'missing hectic finish' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'trots race had first radio broadcast' is the wordplay.
'trots' is an anagram indicator (I've seen 'trotting' mean this (letters walk or trot around)).
'first' says to take the initial letters.
'broadcast' becomes 'ea' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The first letters of 'race had' is 'rh'.
'rh'+'radio'='rhradio'
'rhradio' anagrammed gives 'diarrho'.
'diarrho'+'ea'='DIARRHOEA'

Can you help me to learn more?