Can I use a calculator?

Geometry Level 3

\[\begin{eqnarray} A &=& \tan^{-1} \left( \frac 1 {\sqrt2} \right)+ \tan^{-1} \left( \frac 1 {\sqrt3} \right) + \tan^{-1} \left( \frac 1 {\sqrt4} \right) \\ \\ B & = & \frac {\pi}{2} \\ \end{eqnarray} \]

Without resorting to tables or calculator, determine which of these numbers above is larger.

All credit for this problem goes to Pi Han Goh.

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