两边同取正切:：tan(arctan0.2w-arctan0.02w)=tan(45°)
[tan(arctan0.2w)-tan(arctan0.02w)]/{1+[tan(arctan0.2w)·tan(arctan0.02w)]}=1
[tan(arctan0.2w)-tan(arctan0.02w)]={1+[tan(arctan0.2w)·tan(arctan0.02w)]}
0.2w-0.02w=1+(0.2w)·(0.02w)
0.004w²-0.18w+1=0
4w²-180w+1000=0
w²-45w+250=0
解得：w=(45±√1025)/2
即：w1=(45+√1025)/2≈38.50781059；
w2=(45-√1025)/2≈6.492189406；
验算：⑴ -arctan0.02w1+arctan0.2w1= -arctan(0.02×38.50781059)+arctan(0.2×38.50781059)
= -37.60188958+82.60188958=45º
⑵ -arctan0.02w2+arctan0.2w2= -arctan(0.02×6.492189406)+arctan(0.2×6.492189406)
= -7.39811042+52.39811042=45º
