This question already has an answer here:
Question: $$\tan 9 - \tan 27 - \tan 63 + \tan 81$$
Answer I'm getting : 0
What I did: Well I clubbed together $\tan 9$ and $\tan 81$ and $\tan 27$ and $\tan 63$ (took out negative as common). Then using the identity for $\tan (A+B)$, I rearranged to formula to get what $\tan A + \tan B$ is. With that I'm getting zero multiplied by $\tan 90$. Since anything multiplied by zero, even infinity, is zero, I guess it should be zero.
I'm pretty sure my logic fails me somewhere, please tell me where (probably in the infinity and zero multiplication part)