The transfer function is \$F(p)=10/(p^2+2p+1).\$
Using Wolfram Alpha, the Nichols plot shows that the argument \$\to -\pi\$ when \$\omega \to +\infty\$.
However, calculating the argument on paper gives\$-\arctan(2w/(1-w^2))\$which \$\to 0\$ when \$w \to +\infty\$.
Where is the error, mathematically?