Lol you funny guy (to the pic). Ok I made it. On my third try. Stayed with my old policy and used 2 new tactics.
What I did was taking the early settler of independence and rush to the mountains near constantinople. There behind the mountains and still on the water I founded together with another city for what I have spammed another settler with production my 2 cities. Then all cities build fast swordmen and archers. This way it was possible to hold this position. Theodora was really pissed that I founded my city that close and declared war after only 3-4 turns lol. But however she only tried to attack through the mountains and did only move very few units around. With the rough terrain in addition my archers were well prepared. I have to admit that it was a little bit a critical situation when the dromons came in but once i got my first genreal and founded a citadel the few squares she could move were blocked with heavy damage in addition. At this point I already knew that I probably would win the game.
I also managed it the first time to get Saladin on my side.
First I gave him gold to declare war on Theodora so we had together an enemy.
Then I denounced some other nations for extra friend bonus.
Last I made the friends agreement. It hold until turn 80 but that was enough to build up a huge fleet.
And this was the key (to my success). With an early city the stupid AI moved all its troops and I killed them piece by piece. Building then all other cities on the water I had soon a big fleet to also fight the dromons.
Last I researched straight for ships. Once you got frigates you can take over constantinople. If your southern fleet is not enough build a city in the north to the black sea. There some additional frigates and you should have it. Therefore you will need iron. Lots of it. I was lucky to have founded my cities always near iron so I had 18 piece of it.
However to withstand the first attacks of her and pay Saladin and Austria to make war with the whore (she really was a whore in fact lol) I had to use my first swordman and immediately moved it into west to discover the european nations. When I found them I paid them for war. Sold all my resources and gold per turn to take their gold and made also war with them. Only the british managed it one time to become a bit of dangerous at turn 80. For somewhat they managed to bring down a settler near Aleppo. I have no idea how they did. Probably they were pissed off because I took a lot of gold from them 3 times and each time declared war to gain my luxury resources back immediately. Well without this trick I wouldnt have had the gold to improve my cities fast enough. In the end all hated me but however I made it.
Constantinople was killed at around turn 150.
Still something to add:
Well after winning this one and the Fall of Rome on deity I have to say that a war with deity AI is challenging. But you can totally win it. Especially against just 1 or 2 deity AIs. However the bad thing is that outside of a scenario the AI will outtech you. Thats in my opinion the biggest problem. And the last challenge. I never beat an AI on deity except on a small map one on one after teching up everything over 300 turns
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I guess if you don't know the Four Lads song (later successfully covered by We Might Be Giants in what is apparently their only mainstream hit), it is probably a tad confusing 
