VMO 1984 Problem 2

The sequence $a_1$, $a_2$, $a_3$, ... is defined by $a_1$ = 1, $a_2$ = 2, $a_{n+2}$ = $3a_{n+1}$ - $a_n$. Find $cot^{-1}a_1$ + $cot^{-1}a_2$ + $cot^{-1}a_3$ + ... .