Gollum entering moria

[lathspell]

The tale of Gollum is known to most here. He came out of the mountains, found the trail of Bilbo and traced it and came to Dale. There he discovered the name of the Shire, and he wanted to go there to find the Hobbit who 'stole' his Ring. But something else happened: he made his way to Mordor and was questioned by Sauron. Afterwards he was captured by Aragorn and he asked the Woodelves of Mirkwood to keep him as a prisoner.
Legolas tells in the LotR (The Council of Elrond) that Gollum managed to escape, because of the Orcs that assailed them at unawareness.

In UT it's told that Sauron heard of Gollum being captured and held by the Woodelves. That didn't bother him much, but he also heard of Mithrandir, that he went to Mirkwood to the Elves to have a long talk with Gollum. That troubled him deeply, because he didn't want the Wise to know that the Ring had been found again. (that Mithrandir already knew this, he didn't know). So he let Orcs attack the elves to kill or capture Gollum, or at least to get him out of the hands of the Wise and their allies. Gollum escaped both the elves and the orcs and fled before them. Both the elves and the orcs were following him, and Gollum crossed the River Anduin.
In the meanwhile Gollum gained other followers, for Sauron had send the Nine to seek for two things: Gollum and a land called 'Shire'.
Now, in the UT it is told that Gollum fled for the Nazgûl and his himself in Moria. My question is: how did he enter moria?

The East-gate was watched by orcs as is said in LotR.

They passed into a hall, bright with daylight from it's high windows in the east. They fled across it. Through it's huge broken doors they passed, and suddenly before them the Great Gates opened, an arch of blazing light.
There was a guard of orcs crouching in the shadows behind the great door-posts towering on either side, but the gates were shattered and cast down.

So it seems quiet unlikely that he passed into moria through the east-gate for there were guards who would spot him for I think that even that cunning stealth of Gollum would be spotted by the night- and day-eyes of the Orcs.
The Westgate seems out of the question, thinking of the Magic of the Doors, the Word to open the Doors and the Watcher in the Water.
So both gates seem to be shut for him. Can it be that he found another way in?... in my opinion it would also explain how he came out again, with the bridge broken and him being still at the other side.

What do you people think about this? About how Gollum entered and managed to escape again out of moria?