Final answer:
The patch on the left shoulder of the NWU Type 3 is the 'don't tread on me' patch, symbolizing U.S. Navy pride, heritage, and camaraderie. It features a rattlesnake and historic motto, reflecting military resilience and fighting spirit.
Step-by-step explanation:
The patch on the left shoulder of the NWU Type 3 uniform, which stands for Naval Working Uniform, is the don't tread on me patch, officially known as the Union Jack patch. This patch is emblematic of U.S. Navy pride and heritage. It features a rattlesnake and the motto 'Dont [sic] Tread on Me', which is a historical symbol dating back to the early American Navy and a period when the United States was gaining its independence. The patch is also a source of camaraderie among service members and represents a connection to the Navy's historical resilience and fighting spirit. Its importance lies not just in its symbolism, but also in its ability to foster unity and a sense of shared purpose among the sailors who wear it.