Why is Wolfram Alpha wrong?

I calculated $$\tan 75^o - [\cot 13^o\cdot \cot 23^o \cdot \tan 31^o \cdot \tan 35^o\cdot \tan41^o]$$ and I got a nonzero answer:
http://www.wolframalpha.com/input/?i=tan%2875%29-[cot%2813%29*cot%2823%29*tan%2831%29*tan%2835%29*tan%2841%29]

But someone posted this problem in a forum as an identity, i.e. $$\tan 75^o = \cot 13^o\cdot \cot 23^o \cdot \tan 31^o \cdot \tan 35^o\cdot \tan 41^o$$

So my question is: Should the answer be $0$? And if so, why is Wolfram Alpha giving a nonzero answer?

Thanks!

• Maybe WolframAlpha interprets the inputs as radians, not degrees. Verify that... – cjferes Sep 25 '14 at 19:31
• look at the numberline – ganeshie8 Sep 25 '14 at 19:32
• Besides the above explanations, WA is, astonishing (?) enough, not infallible: it makes mistakes, and quite a few, when trying to do some stuff. Be careful with that. – Timbuc Sep 25 '14 at 19:33
• @AnalysisIncarnate If Mathematica gives you $0$, then it's (almost certainly) a rounding error, since WA doesn't use the full power of symbolic manipulation and therefore computes the product as a floating point value. – Daniel Fischer Sep 25 '14 at 19:39
• Probably not a coincidence. Playing around with the addition theorems may lead to the goal. – Daniel Fischer Sep 25 '14 at 19:55