When we learn Torah we do everything we can in order to understand. The Torah was given in order to be comprehended by the human mind. When it comes to tragic events we are often in a realm that is far beyond us. We CAN'T understand. There is no theological problem with the horrible tragedy of the three boys that wasn't already presented when 5,999,997 more people were brutally murdered 70 ago.
Nistarim darkei Hashem. We just don't get it and we are not supposed to. Aharon Hakohen couldn't understand why on the joyous day of the chanukas hamishkan his beloved sons were taken. His reaction? Silence. וידם אהרן. Silence allows one to try to listen and perceive the Divine lessons instead of philosophizing. We can't fully understand but we MUST try to learn lessons. In other words - the abstract question of "why" will remain unanswered [in this world] but the "what" [should we do] should be addressed. The Rambam says [hil. taaniyos] that it is CRUEL to say that tragedies happen by chance because that generates more tragedies.
There are much greater people than I who will try to bring out lessons but at the risk of going out of my orbit - I will offer the following....
The first thing we should do is teshuva. Teshuva, among other things, for being so self-centered. Hashem made something happen to extract people out of their narrow world of selfish concerns and enabled us to identify with the unspeakable suffering of others.
Two - This event brought Jews of all stripes, kippah sizes and colors, together [even Yair Lapid said he turned his house upside down in order to find a siddur and daven! His wife, incidentally, is the great-grandaughter of one of the sharpest lamdanim of the previous century. If you don't know who Yair Lapid is - I envy you:-). If you never learned the sefarim of his wife's great-grandfather - I pity you]. We can remain united because at the end of the day we all have common concerns. Not the least of which is to survive in this jungle we call the planet earth when so many want to devour us just because we are Jewish.
If you find yourself apathetic and still overly concerned with your own personal problems then it would be good to watch the funeral and cry a bit. If you are terribly shaken then it is time to strengthen yourself in the middah of simcha. The Baal Shem Tov and his followers stressed the necessity of simcha in ALL situations. After a very close chossid of the Tolna Rebbe Shlita suddenly passed away at a very young age and left a huge brood of orphans, the first thing he said to me when he saw me was "Reb Elchonon, we only go with simcha". He once spoke at a gathering in memory of a young child who was tragically killed in a freak accident and emphasized the middah of simcha. Depression is a weapon of the powers of evil.
There is much more but I will leave it at that. One more thing though - Every single word of tefilla was registered in shomayim and made it's mark. It will help in the future in ways we won't know and will be a source of tremendous merit for the neshamos of the three kedoshim forever. NO tfilla is ever lost.
We should all know no more tzaar and Hashem should comfort the families of the three boys and they should have the strength to get through this and see much simcha. They all made a tremendous Kiddush Hashem with their display of Emunah throughout. They are the real heroes.