world problem please help! Trigonometric Ratios and Special Angles

So this is basically the question

matt is flying his kite at the end of a 40 meters string. The string makes and angle of pi/4 with the ground. The wind speed increases, kite flies higher until the string makes an angle of pi/3 with the ground.

Question:

Determine an exact expression for the horizontal distance that the kite moves between the two positions.

So far I got this

X2=40

---

√2

X1=20

Now im just subtracting these two and I got this

40-20√2

-----------=the diference but my books answer is 20 (√2-1)

√2

I would like to know how the book got that answer, I think my answer just needs to be simplfy but I cant get the same answer. When i calulate both i get the same answer. Please help!! this is really bothering me!!!