math -- linearly independent arctans

For n in N, let a_n = arctan(1/n).

Let V be the vector space, over Q, generated by {a_n | n in N}.

Questions ...

(1) Is V is infinite dimensional?

(2) Assuming the answer to (1) is yes ...

Let S be the set of indices n such that a_n is linearly independent of
{a_k | k < n}. Is there a simple algebraic characterization of the
elements of S? If not, is there at least an effective procedure to
determine, for a given n in N, whether or not n is in S?

quasi
.

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