Find the eigenvalues for the following matrix:

A=

1 2 2 2

2 1 2 2

2 2 1 2

2 2 2 1

det(A-λI)=

1-λ 2 2 2

2 1-λ 2 2

2 2 1-λ 2

2 2 2 1-λ

Is there a shortcut to computing this? Or do I need to take (1-λ)det(3x3 matrix)-(2)det(3x3 matrix)+(2)det(3x3 matrix)-(2)det(3x3 matrix)?