ДОПОМОЖІТЬ РОЗВ'ЯЗАТИ ↓↓↓ /(О^О)\ arctg(x+2)-arctg(x+1)=π/4

Решите задачу:

$arctg(x+2)-arctg(x+1)=\frac{\pi}{4}\\\\tg(arctg(x+2)-arctg(x+1))=tg\frac{\pi}{4}\\\\tg( \alpha - \beta )= \frac{tg \alpha -tg \beta }{1+tg \alpha \cdot tg \beta } \\\\ \frac{tg(arctg(x+2))-tg(arctg(x+1))}{1+tg(arctg(x+2))\cdot tg(arctg(x+1))} =1\\\\ \frac{(x+2)-(x+1)}{1+(x+2)(x+1)} =1\\\\ \frac{1}{x^2+3x+3} =1\\\\x^2+3x+3=1\\\\x^2+3x+2=0\\\\x_1=-1\; ,\; \; x_2=-2\; \; (teorema\; Vieta)$