You must show your opponent the monster you select from your Deck for this card’s effect. If you have no eligible monsters, your opponent gets to see your Deck to verify.
The effect of “Sangan” only activates when it is sent from the field to the Graveyard, not from your hand or Deck, and not if it is removed from play.
If the Summon of this card is negated with “Horn of Heaven” or “Solemn Judgment” you do not get its effect.
If you control your opponent’s “Sangan” and it is destroyed, your opponent gets the effect since it activates in his/her Graveyard.