Trim phyllo sheets to fit the pan you will be using (9x13) or a rectangular pan with a similar capacity, with 2.5" sides. (Don't use a nonstick pan--it will get ruined when you cut out the baklava.) Keep phyllo sheets covered with a slightly damp towel.
In a bowl, stir together the butter/margarine and the oil. Drizzle a few tablespoons on the pan bottom. Center 1 sheet phyllo on the bottom of the pan. Brush generously with butter and oil. Continue layering phyllo sheets, brushing each generously, for a total of 8 sheets.
Sprinkle 1/3 of the nuts over the top.
Continue layering phyllo leaves this way, sprinkling with nuts after another 8 sheets, then 4 more leaves, more nuts, and the remaining leaves, always brushing each sheet generously before you place the next one in the pan.
Brush the top layer with the butter/oil mixture. Using kitchen scissors or a very sharp knife, cut the pastry into diamond shapes, cutting only halfway through the pastry. (Diamond shapes are achieved by cutting 5 or 6 horizontal rows, then cutting diagonally across these rows to form diamonds).
Bake for 1 hour, or until pastry is golden brown. Meanwhile, make the syrup.
To make syrup: In a saucepan, combine the syrup ingredients and heat until the sugar dissolves. Bring to a boil and simmer for about 5 minutes. Cool to room temperature before pouring evenly over the pastry. Let the baklava sit for 1 hour or overnight before serving.