MHB Solving System of Equations with x,y,z in [0,pi/2)

[juantheron]

How can i solve system of equations , if x,y,z\in \left[0,\frac{\pi}{2}\right)\begin{cases}\tan x+\sin y+\sin z = 3x\\\sin x+\tan y+\sin z = 3y\\\sin x+\sin y+\tan z = 3z\end{cases}

 

[soroban]

Hello, jacks!

How can i solve system of equations , if x,y,z \in \left[0,\tfrac{\pi}{2}\right)

\begin{array}{ccc}\tan x+\sin y+\sin z &amp;=&amp; 3x\\<br /> \sin x+\tan y+\sin z &amp;=&amp; 3y\\<br /> \sin x+\sin y+\tan z &amp;=&amp; 3z\end{array}

I don't think you can.
. . The equations are transcendental.

However, by inspection, (x,y,z) \,=\,(0,0,0) is a solution.