# Inverse trigonometry or number theory

Geometry Level 4

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

If the ordered pair of natural numbers $(a_1,b_1)$ and $(a_2,b_2)$ satisfy the equation above, find the minimum value of $a_1+b_1+a_2+b_2$.

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