A quadrangulation is a 2-cell embedded graph where every face is a quadrangle. An even triangulation is a 2-cell embedded graph where every face is a triangle and every vertex degree is even. A triangulation on the sphere is 3-chromatic if and only if it is an even triangulation. In this talk, we show that any quadrangulation can be extended to an even triangulation by adding diagonal edges to all quadrangle faces. We also determine the number of distinct even triangulations. This is joint work with Atsuhiro Nakamoto and Kenta Ozeki.