Kwang Il Kim
page 26 says that Gothmog's die is removed if...
"Either its Army result or its Eye result (which show the remove symbol) was chosen and the Witch-king (any version) is in play, OR
The Witch-king, the Black Captain is in play."
I don't understand why the first part says "Witch-king (any version)" - why doesn't it just say "The Witch-King, Chief of the Ringwraiths"?
b) if a result with a remove symbol is chosen and the Witch-king is in play, or
c) if any result with/without a remove symbol and The Black Captain is in play
Gothmog's die will be removed.
But the die won't be removed from the game only if you choose a die without a remove symbol and the Chief of Ringwraiths is in play.
So the presence of the Black Captain always removes Gothmog' die while the Chief of Ringwraiths only does with a die result showing a remove symbol.