It's improper maintenance, Bermuda should never get over 2 in.

Yea, you may be better off scalping it down to 1/4" to let the sun get in. From there start feedings with organics (corn/alfalfa/etc) and water more conservatively. You would do well to find a better maintenance height after new growth occurs. I think reeljake maintains his at 1" mowing once every 7 days. Just never let it get out of control again. If maintaining at 1" you will have to mow before it reaches 1.5" (never mow more the 1/3rd rule).

I have a friend in Gilbert, AZ who fought my suggestion for years. His bermuda lawn never looked good. He had a shade problem and so do you. He finally took my suggestion to put in St Augustine. Now it looks like this...

Proper watering is the mistake most people make. Here's more on watering...

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.