Series circuit LED controlled by Arduino schematic question
Use the Arduino's 3.3V rather than a 7.5V supply.
Power each LED separately each with its own resistor rather than all three in series.  Wire them as common cathode.
Use LEDs with high luminous efficiency to reduce the current.
Just because an LED is rated at 20 mA does not mean you have to run it at 20 mA.
With a high luminous intensity LED you can likely reduce the current to 1 mA and still have a fairly bright LED. 

Use a 22,450 mcd Cree C503B at 1 mA you will still have over 1,100 mcd and the ATmega only has to sink 3 mA.    

With three LEDs wired common cathode the ATmega could sink 6 mA per LED at 6,700 mcd.
If 6,700 mcd is not enough, double them the up (six LEDs) and use the 5V supply.

If you can use surface mount LEDs use Luxeon Color C, OSRAM Oslon SSL 80, or Cree XP-E.