i think mass effect 2 shows you how did sheperd save the galaxy from collectors and new cerberus organization.

In game in mass effect 3 cerberus relationship continued in rough manner but we came close to the alliance a human military in game as we are in first game as alliance military operative and become spectre in first and third game.

In my own words and analogy, its like you wake up in the morning and done all the stuff and gotten ready for work but forgot to take breakfast such as comparable to mass effect 1, secondly its your lunch time you again forget to take lunch such as comparable to mass effect 2 game, thirdly you got to dinner and you suddenly realized that you forgot about  breakfast and lunch ,...then you with great hunger and thirst do the dinner to remove your hunger now remember dinner is mass effect 3 game so this is totally incomplete that you can skip your meal of day time to time so mass effect trilogy is same as meal which you should play equally all to achieve satisfaction and interest of getting out all three ,.... All three games are good and give you great fun and exploration of galaxy through out game so remember playing mass effect 3 would be like leaving two important meal such as break fast and lunch which would let your hunger explode to know more when ever you get chance you should play all three of them