Let \( a_{1}=1, a_{2}, a_{3}, a_{4}, \ldots \) be consecutive natural numbers. Then \( \tan ^{-1}\left(\frac{1}{1+a_{1} …

Let \( a_{1}=1, a_{2}, a_{3}, a_{4}, \ldots \) be consecutive natural

numbers.

Then

\( \tan ^{-1}\left(\frac{1}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{1}{1+a_{2} a_{3}}\right)+\ldots+ \)

\( \tan ^{-1}\left(\frac{1}{1+a_{2021} a_{2022}}\right) \) is equal to