This episode of history confuses me to no end. I can't understand why they would have declared war on the U.S
Here's a post I wrote a couple months back on this subject:
The United States had been waging an undeclared war against Germany for months, if not more, by December 1941. From Lend-Lease (arguably an act of war in itself) to using the US Navy to protect shipping to the UK, to the US Navy actually shooting at German ships in the process.
When Japan attacked the US Hitler was elated, and decided this was as good a time as any to take the gloves off and go to war. In the best-case scenario US aid to the British would be cut (as well as most US aid to the Soviets) and they could be effectively put out of the war while the US was preoccupied with fighting the Japanese first. Then if, the United States ever did turn its attention to Europe Germany would have conquered most of Russia by that time and incorporated its resources into Germany's war effort (conceivably sufficient to fend off any Anglo-American attacks).
Unfortunately for Hitler, FDR agreed with Churchill that Germany was the more dangerous opponent and had to be eliminated first, so the strategic gamble failed.
As for Mussolini, it should be noted that Italy was severely dependent on German help in its war effort by December 1941. And at that time, with the Wehrmacht at the outskirts of Moscow it looked like The Axis Powers were going to win the war, especially now that Japan was seemingly going to draw the United States away from the European war. By declaring war along with Germany, Italy would have a more legitimate claim to the spoils of victory.
Three days before Pearl Harbor, the Rainbow Five War Plan was leaked and published in two US newspapers.
Rainbow Five was FDR's plan for fighting WW2. It foresaw increased US action, culminating in landings in Europe by late 1943 or 1944. Basically, it showed that the US was already on a war footing. All that remained to be determined was the matter of timing. By declaring war instead of waiting for the US to initiate hostilities, Germany was able to engage in unrestricted submarine warfare against the US. This was the only theater of action where the two nations forces were in contact. The big gamble was that Germany would have finished off the USSR by the time the Americans were ready to engage.