arctan " or " tan^(-1) are both the same thing.
Tangent is the numeric value you obtain if you have ("opposite")/("adjacent") for a right triangle. In other words the amount of 'up' for 1 'along'. It is the gradient value of the hypotenuse
Ok! we have now established what a tangent is so what is tan^(-1)? Put simply it is the process of reversing the numeric tangent value back into the angle between the hypotenuse and the adjacent.
tan(3 pi/5) converts the angle of 3 pi/5 into the gradient.
tan^(-1) " of " tan(3 pi/5) reverses the process. So if you have
tan^(-1)(tan("something") the tan^(-1)(tan() cancel each other out and you are left with just the angle that you started with.
so tan^(-1) (tan(3 pi/5)) =3 pi/5
