Then: △CPP' is an isosceles right triangle.
∴PP'^2=PC^2+P'C^2=2^2+2^2=8
P'A^2=PB^2= 1
PA^2=3^2=9
∴PP'^2+P'A^2=PA^2
∴∠AP'P=90
∴∠bpc=∠ap'c=∠ap'p+∠pp'c=90+45 = 135