In order to collect the three pieces of Trident, you will have to go to the Shrine of Sea God first. Before going there, there is a key item you need to collect. Go to the north of the village and enter the sanctum. There is a drop of water you could not reach before. With Piers, you can Frost two puddle of water to make two ice pillars for you to jump across. Take the Sea God's Tear and leave.