I'd still like to know what it's for, and why it needs the accurate phase relationship - or even to confirm that it does!.
But for a single chip, cheap solution, you could use a PIC12F675, 8 pin PIC with 10 bit A2D.
Sample the triangle wave coming in, if it's below a certain (low) value set the output high, if it's above a certain (high) value set the ouput low. This will give the correct phase relationship - and with the slow frequency of the triangle wave will be much more than accurate enough.
Perhaps a bit of overkill, but it only requires one cheap 8 pin PIC, and no other components (assuming you already have a 5V supply - but any solution will require a supply).