How to win a winnable game.

Today i'd like to post some reflexion about tactical practice.

Somehow tactical exercises are often a clear material advantage acquired after the tactical blow, subject of the puzzle.
In the one below, the author overlooked a crushing defense for black who is under attack, but still you can win the game with white pieces.

Let's try to do it by yourself, if you need to practice endgames, then it is very well suited for you too !
You will discover that it can be a difficult task to win a game which is supposed to be winnable.
My solution is one among others, maybe (surely) you can find a shortest way to win.

Here is the initial FEN position :
"4rb2/3q1ppk/3p2np/1p1P3Q/1P1B2NP/3PR3/3r2P1/2R3K1 w - - 0 1"



You can download the PGN file here if you prefer :
http://cjoint.com/data/lDnzgFQ0O1.htm

My conclusion would be that doing the queen sacrifice at the beginning cannot be calculated till the end, so somehow, you have to believe enough in it, to do it ! And foresee the general ideas behind it, there will be exchange of queens, R vs B+P ending, get rid of the annoying knight, and so on... to help you believing in it.

... gxQ, Nf6+ gives some kind of windmill motive i think so eventually i would have seen Qxh6+ but it would take me a whole time to actually find it since me and sacrifaces arent buddies yet.