The value of \(tan^{-1} \left(\frac 1{1 + a_1a_2}\right) + \tan^{-1} \left(\frac 1{1 + a_2a_3}\right) + ....+ \tan^{-1} \left(\frac 1{1 + a_{2021}a_{20222}}\right)\) if a1 = 1 and ai are consecutive natural numbers
(1) \(\frac \pi4 - \cot^{-1} (2021)\)
(2) \(\frac \pi 4 - \cot^{-1} (2022)\)
(3) \(\frac \pi4 - \tan^{-1} (2021)\)
(4) \(\frac \pi 4 - \tan^{-1}(2022)\)