Suppose E is a projection in M_2(C) with rank one. Show that there is a real number θ and a complex number β with |β| = 1 such that

E =

cos^2 βsinθcosθ

Bsinθcosθ sin^2 θ

M_2(C) represents an 2 x 2 matrix in the complex numbers.

Β represents β conjugate.