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If a^2+b^2+c^2=1 then show that value of...

If `a^2+b^2+c^2=1` then show that value of the determinant `|a^2+(b^2+c^2)costhetab a(1-costheta)c a(1-costheta)a b(1-costheta)b^2+(c^2+a^2)costhetac b(1-costheta)a c(1-costheta)b c(1-costheta)c^2+(a^2+b^2)costheta|` simplifies to `cos^2theta`

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Prove that : (1-costheta)(1+costheta)(1+cot^(2)theta)=1

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