Does this property hold for inverse too) (Part-V)

Let $\arctan{x} = ß$ . If we draw a right triangle where the side opposite to $ß$ is $a$ and the side adjacent to $ß$ is $b$ , then $x = \tan(ß) = \frac{a}{b}$ . Now, ß = 1/arccot(x) = 1/arccot(a/b) If we take $\cot((π/2)-ß)$ , we get $\frac{a}{b}$ . Thus, arccot(a/b) = (π/2)-ß. By substitution, $ß = \frac{1}{((π/2)-ß)}$ , meaning that $-ß^2 + (π/2)ß - 1 = 0$ . The discriminant comes out to be $(π^2/4) - 1 < 0$ , meaning that there are no values of $ß$ satisfying the original equation. No calculus requried!