What is "Z" - Alphas, LaTex & MathType Explored

[bomba923]

I wish I knew LaTex . But I know MathType!

Does such a pair of alphas exist?? (See the Below Thumbnail/attached image)
"Z" is the set of all integers

 

[Zurtex]

LaTeX is really easy to learn, just click on stuff people have wrote and it will show you the code. Check this thread out: https://www.physicsforums.com/showthread.php?t=8997

Correct me if I am wrong but your question simplifies down to:

$$\text{If} \, \alpha_1 \in \mathbb{Q} \, \, \, \text{does} \, \exists \, \alpha_2 \in \mathbb{Q}$$

Such that:

$$\tan \left( \alpha_1 \right) + \tan \left( \alpha_2 \right) = \frac{\pi}{3}$$

I'd guess not but to be honest I have no idea.

Oh and I think the question is wrong otherwise you could always let k=0.

 

[Curious3141]

Are we sure that that is supposed to be a tangent and not an arctangent ? I don't know of any "special" identities involving the arctangent of multiples of pi. The term in pi looks more suited to be the argument of the tangent function.

 

[Zurtex]

Let $\alpha_1 = 1^c$

That should solve the problem.