The Public Theater did not take the easy route with its selections for this summer’s Shakespeare in the Park season, such as programming a top-tier tragedy followed by a crowd-pleasing comedy or a musical. Instead, it produced an all-female production of the ever-discomforting “The Taming of the Shrew,” which is being followed by the similarly difficult “Troilus and Cressida.”

Traditionally classified as a tragedy but really more of a “problem play,” it resembles a sour variation on “Romeo and Juliet” in which the romantic escapades are played out during the Trojan War instead of a mere family feud.

Troilus, a Trojan prince, awkwardly woos the standoffish Cressida by using her uncle Pandarus as an intermediary. Meanwhile, the Trojan leaders attempt to justify a long, bloody conflict based upon Paris’ hasty abduction of Helen, and the Greek commanders plot to motivate the moody warrior Achilles into rejoining the war effort. All the while, the Greek soldier Thersites acts the part of the fool and offers bitter commentary.

The play is choppy and long (running three hours). But Daniel Sullivan, who has directed many shows in the park, delivers a smart production that views the ancient conflict from a contemporary standpoint. For instance, as the noble Hector preps for battle, a documentary crew is on hand to film him. The industrial set design is easily shifted to represent different settings.

Sullivan does not shy away from suggesting that Achilles and his companion Patroclus are more than just friends, or that Cressida is sexually assaulted when she arrives at the Greek camp. The battle scenes are built up with fight choreography, weaponry and splattered blood.

Standouts in the large cast include Corey Stoll’s business-minded Ulysses, John Douglas Thompson’s jocular Agamemnon, John Glover’s dapper but frail Pandarus, Alex Breaux’ overactive Ajax, Bill Heck’s conflicted Hector and Andrew Burnap’s sulky Troilus. As Cressida, Ismenia Mendes draws a full character arc out of a problematic role.