Denis O’Hare has signed on to appear opposite Amy Adams in the Public Theater’s upcoming Shakespeare in the Park production of tuner “Into the Woods.”O’Hare (“True Blood,” “American Horror Story”) will play the baker whose wish for a child is a key component in the plot of the fairy tale-mashup musical. Adams is onboard as the baker’s wife. O’Hare joins a previously announced ensemble that also includes Donna Murphy, Jessie Mueller, Gideon Glick and Ivan Hernandez. Timothy Sheader helms with co-director Liam Steel, both of whom staged a popular outdoor staging of “Into the Woods” in London in 2010. A 1987 musical by Stephen Sondheim and James Lapine, “Into the Woods” is the second offering of the summer season at Shakespeare in the Park. First up is “As You Like It,” which runs June 5-June 30. “Woods” begins perfs in Central Park July 23 ahead of an opening set for Aug. 9.