How to find the value of

Question

arctan(2 sin (pi/3))
without using calculator or sketching a triangle. It is like taking u=something and then evaluating.

Thanks.

the solution relies on the fact that you should know the ratio of sides of the 30,60 90 degree triangle, and knowing that Pi/3 = 60 and pi/6 = 30º

in pi/3 = √3 /2 so 2 sin pi/3 = √3 or √3 /1

now what is the angle so that tan(angle) = √3 ???
must be 60º or in radians pi/3