If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi \), then
(1) \( x^{2}+y^{2}+z^{2}+2 x y z=1 \)
...
If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi \), then
(1) \( x^{2}+y^{2}+z^{2}+2 x y z=1 \)
(2) \( 2\left(\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z\right)=\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z \)
(3) \( x y+y z+z x=x+y+z-1 \)
(4) \( \left(x+\frac{1}{x}\right)+\left(y+\frac{1}{y}\right)+\left(z+\frac{1}{z}\right) \geq 6 \)
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