Question: Eigenvectors of 2x2 Matrix with trig functions

How can I evaluate the eigenvectors of a 2x2 Matrix with trig functions as entries? This is what I did: with(LinearAlgebra): K:=<<cos(theta)|sin(theta)>,<sin(theta)|-cos(theta)>>; Eigenvectors(K); Error, (in LinearAlgebra:-LA_Main:-Eigenvectors) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values I'm wondering why cos(theta) shouldn't be an algebraic function ?? Assuming theta to be real I get the same.
whattype(K);        Matrix
K[1,1];             cos(theta)
whattype(K[1,1]);   function
is(K[1,1],algebraic);      true
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