Inverse trigonometry or number theory

Geometry Level 4

arccot(8)=arctan(a)arctan(b)\large \text{arccot} (8)=\arctan (a)-\arctan(b)

If the ordered pair of natural numbers (a1,b1)(a_1,b_1) and (a2,b2)(a_2,b_2) satisfy the equation above, find the minimum value of a1+b1+a2+b2a_1+b_1+a_2+b_2.

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