### Commentary on "Simplify trig expressions with the double angle formula"

A bit of reflexion leads me to propose a "brute force" answer to a question wher the answer could be divined with a bit of "intuition".

The original question was :

I am trying to simplify the following
expression in sage:

(sqrt(3)/3*cos(x)+1/3*sin(x))

the resulting expression should be:

2/3*cos(pi/6-x) .simplify_full(),
trig_reduce(), or simplify_trig()
cannot produce this simplification.

Is sage currently capable of doing
this?

See below for the steps of the solution. Comments, criticisms and even lazzi welcome...