The hard determinant

By direct expansion, the value of the determinant is $(\cos^2 2019\degree+\cos^2 1131\degree)^2+(\cos^2 1869\degree+\cos^2 1101\degree)^2+2(\cos 2019\degree\cos 1101\degree-\cos 1131\degree\cos 1869\degree)^2+2(\cos 2019\degree\cos 1869\degree+\cos 1131\degree\cos 1101\degree)^2$ . Now $\cos 2019\degree=-\cos 39\degree, \cos 1131\degree=\cos 51\degree=\sin 39\degree, \cos 1869\degree=\cos 69\degree, \cos 1101\degree=\cos 21\degree=\sin 69\degree$ . Substituting all these we get the value of the determinant as $1^2+1^2+2\times 1^2+2\times 1^2=\boxed 4$ .