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The tangent half angle formula, one of several, is
We have θ is opposite 4 in the 3/4/5 right triangle so
Answer: 1/2
This is actually pretty deep. It says half the big acute angle in the 3/4/5 triangle is the small diagonal angle of the 1x2 rectangle. Similarly, the small acute angle in 3/4/5 triangle is twice the small diagonal angle of the 1x3 rectangle.