Position racks in the top and bottom thirds of the oven and heat the oven to 375°F In a large bowl, combine the spinach, feta, mint, sun-dried tomatoes, olives, eggs, garlic, lemon juice and zest, pepper, and salt. Mix well.
Unroll the phyllo and lay it flat on a clean, dry surface. Cover completely with plastic wrap. Working with one sheet of phyllo at a time, and keeping the rest covered with the plastic wrap to keep it from drying out, place a sheet vertically in front of you. Brush the phyllo with butter and cover with another sheet. Butter the top sheet and cut the phyllo lengthwise into equal 3-inch-wide strips. Spoon 2 teaspoons of filling on the lower end of each strip as shown in the left photo below. Fold up the phyllo strips as you would a flag to create a neat triangle, being careful not to roll too tightly or the triangles will crack when baked. Transfer to a baking sheet and cover with plastic. Repeat with the rest of the phyllo and filling until you run out of filling.
Butter two sheet pans. Arrange the phyllo triangles on the prepared baking sheets in a single layer. Brush the tops of the triangles with melted butter and bake until golden brown, 15 to 20 minutes, switching the positions of the pans halfway through baking.
Make Ahead Tips. Assembled, unbaked phyllo triangles can be frozen for up to a month. Freeze the triangles on the baking sheet. When frozen, transfer them to an airtight container, setting parchment or plastic wrap between layers if needed, and return to the freezer. Bake as directed above (do not thaw the triangles first); baking time will be 20 to 25 minutes.