I'm not proposing a total rewrite, just to condense the main points so you don't have to remove that one paragraph in its entirety. I'm proposing Ling.Nut-Lite. I just don't think removing that whole paragraph is the best solution. I want to condense it to just the main points, leaving certain details for further discussion in the body. Here's what I propose so far:

The Six Day War or June War..., also known as the 1967 Arab-Israeli war or the Third Arab-Israeli War, was fought between 5 June and 10 June, 1967 by Israel and the neighboring states of Egypt [then the United Arab Republic, UAR], Jordan, and Syria. At the war's end, Israel had seized the Gaza Strip and the Sinai Peninsula from Egypt, the West Bank and East Jerusalem from Jordan, and the Golan Heights from Syria.

After the 1956 Suez Crisis, Egypt agreed to the stationing of a United Nations Emergency Force (UNEF) in the Sinai to ensure compliance with the armistice agreement and prevent raids across the border . On 4 November 1966, Syria signed a mutual defense agreement with Egypt. Nine days later, Israel attacked the city of as-Samu in the Jordanian occupied West Bank in response to raids from the fedayeen group Fatah. King Hussein of Jordan criticized President Gamal Abdel Nasser of Egypt for failing to come to Jordan's aid and "hiding behind UNEF skirts" [I checked Oren p. 135 and there's no mention of this on that page; please help double check source and find reference - possible later printing is different, I have 2003 first edition].

On 14 May 1967, Nasser began sending Egyptian forces into the Sinai Peninsula. Two days later he requested and obtained the withdrawal of UNEF from Egyptian territory. Israel rejected a proposal to restation UNEF on its side of the border. Egyptian forces replaced UNEF positions at Sharm el-Sheikh in the southern Sinai overlooking the Straits of Tiran. Between 18 and 20 May Israel reiterated declarations made in 1957 that any closure of the Straits would be considered as a cassus belli, or justification for war. Nasser declared the Straits closed to Israeli shipping on 22-23 May. On 1 June, Israel formed a National Unity Government by widening its cabinet, and on 4 June the decision was made to go to war. The next morning, Israel launched Operation Focus, a large-scale surprise air strike that was the opening of the Six Day War.

I think following this, since the lede really only mentions the war between Israel and Egypt, there should be a brief discussion of the Jordan and Syria fronts, as well. With this slimmer version, it should be possible to fit that in, at least briefly. Let me know what you think.