Hello, metlx!

Your work is quite good,

but it can be done more simply than you think . . .

what is the angle between: .

And we get: .

Substitute into [1]: .

We have four intersections: .

We will use this theorem . . .

. . Given two lines with slopes and ,

. . the acute angle between them is given by: .

Differentiate [1]: .

Differentiate [2]: .

At

Hence: .

. . Therefore: .