The Micronesian Kingfisher, Halcyon cinnamomina, has a cinnamon-colored face. In some birds, the color continues onto the chest, producing one of three patterns: a circle, a shield, or a triangle; in other birds, there is no color on the chest. A male with a colored triangle was crossed with a female that had no color on her chest, and all their offspring had a colored shield on the chest. When these offspring were intercrossed, they produced an F₂ with a phenotypic ratio of 3 circle: 6 shield: 3 triangle: 4 no color.

(a) Determine the mode of inheritance for this trait and indicate the genotypes of the birds in all three generations. 

(b) If a male without color on his chest is mated to a female with a colored shield on her chest and the F₁ segregate in the ratio of 1 circle: 2 shield: 1 triangle, what are the genotypes of the parents and their progeny?