@Preben Alsholm Thank you very much for explaining. But I'm still wondering how can the "allvalues" function yield the whole set of exact solutions?
Which algorithm is applied?

Is it correct that it yields the whole set of solutions, and for each set, the root is described in the form of non-linear equations? and it is the simple polynomial, so that we can use the numerical method from this point?

I still don't know how can it works so good like that. I couldn't find any clear explanation for this function.

@acer as Markiyan said: in the real range [-2*Pi, 2*Pi], you double the solution. because cos and sin are only varied from [0,2*Pi] or [-Pi, Pi]

Markiyan Hirnyk

@Preben Alsholm Thank you very much for your fast replying, I didn't know that we have the function allvalues in Maple. Do you know what the algorithm behind the function "allvalues"?

It could be some sort of Newton methods,....., isn't it?

As I know numerical methods can't search for all solutions of non-linear equations as well as the system of equations. Therefore, I'm so curious how the function in Maple can work out on it