Using fsolve() to solve non-linear system equation

[teerasak]

Thank you, parisse. Got your point.

Yes, in fact, this system equation can be solved by solve(). I would like to explore fsolve() as sometimes, solve() cannot provide find all solutions.

For example, if I want to find the solution of the following system equation:
x+y =5*Pi/4
tan(x)=1
Given x,y = 0..2*Pi

solve({x+y=5*Pi/4, tan(x)=1},{x,y}) this gives [Pi/4, Pi].

However, there are some other solution too e.g [5*Pi/4, 0]. How can I find that another solution is [5*Pi/4, 0]?

Because of this, I started finding out another command to search for more complete solution.