Solving a system of two trigonometric equations

[Loaded dice]

So, in our Control Engineering classes, in the presentation about synthesizing a regulator using Bode plot (using lead compensation and lag compensation), we have the following system of equations:

omega_lb1 / omega_ln1 = 12.6
atan(2 / omega_lb1) - atan(2 / omega_ln1) = -6 deg

Allegedly, the solution is:

omega_lb1 = 0.2 rad/sec
omega_ln1 = 0.016 rad/sec

But how can that system of equations be solved?

obviously we have omega_lb1 = 12.6 * omega_ln1, we replace omega_lb1 in the second equation and we get :

arctan(2/12.6*omega_ln1) - arctan(2/omega_ln1) = -6

Now set x = 1/omega_ln1, you get : arctan( (2/12,6) * x) - arctan(2x) = -6

Now recall that if |xy| < 1, then arctan(x)+arctan(y) = arctan ((x+y)/(1-xy)), use this (with arctan(-x) = -arctan(x)) to get the solutions.