<s>[INST] Calculating $\tan15\cdot \tan 30 \cdot \tan 45 \cdot \tan 60 \cdot \tan 75$  What is $\tan15\cdot \tan 30 \cdot \tan 45 \cdot \tan 60 \cdot \tan 75$  equal to (in degrees)?
Here is how I tried to solve it:
I assumed $x = \tan 15 (x= 0.27)$, so I rewrote it as:
$x\cdot 2x \cdot 3x \cdot 4x \cdot 5x = 120x^5$
$0.27^5 = 0.001323$
$120 \cdot 0.001323 = 0.16$
But Google Calculator gives me  $-1.19576279$
What is the right way to calculate this  trig expression?
 [/INST] EDIT : Arturo's solution is really cool. Use that instead, I'll let my solution stay just as a reference.
$$\tan(2A) \neq 2\times \tan(A)$$
You might want to read/revise double angle formulas.
Assuming you need to do this without a calculator,
$$\begin{align*}
 \tan 30 &= \frac{1}{\sqrt{3}}\\
 \tan 45 &= 1\\
 \tan 60 &= \sqrt{3}\\
 \tan 60 &= \sqrt{3}\\
\tan(A+B) &= \frac{\tan(A)+\tan(B)}{1-\tan(A)\tan(B)},\\
\tan(15+15) &= \tan(30) \\
&= \frac{1}{\sqrt{3}} \\
&= \frac{\tan(15)+\tan(15)}{1-\tan(15)\tan(15)}
\end{align*}$$ 
Solving $\frac{2x}{1-x^2} = \frac{1}{\sqrt{3}}$ will give you x = 0.2679
Similarly, you can write $\tan(75) = \tan(90-15)$ and you can work out the product.
</s>