Your insect is the Green June Beetle.  While impressive in size, they are not nearly as damaging as are some of the smaller scarab beetles.  Their grubs are larger also, and although the grubs generally occur in lawns, they do not feed on grass roots, they feed on organic matter.  The adults can be serious pests in vineyards, but they do little noticeable damage in home landscapes.  They are clumsy fliers and can be quite amusing in their behavior.  No treatment is necessary.
LS