[bonanova]

OK this is a little off beat, but it points out an interesting geometrical result.

The problem is to [describe how to] construct an equilateral triangle.

Your tools are

1. Pencil
   
2. Straight edge
   
3. A device that trisects angles
   

I can think of two ways - one is pretty simple.

Post it if you think of it, but there's another way that's perhaps unexpected. [same tools]

Using the pencil as a pencil, the straight edge as a straight edge...

i.e. no arcs, etc.

[bonanova]

If OP had told that the trisector could work for only in acute angles (<90⁰), our first solutions wouldn't work, and maybe would lead us to get closer to solution. Though nothing can halp me to discover it.

Acute angles would limit the triangle you start with.

The process works with say a 30 - 70 - 110 triangle.

Google morley's theorem proof for more on this.

Here's a beautiful demo.