Involving sin^{-1}(z+1/z-1)

Involving sin^{-1}(z+1/z-1) and tan^{-1}((-z)^{1/2})

Involving sin^{-1}(z+1/z-1) and tan^{-1}(1/(-z)^{1/2})

Involving sin^{-1}(z+1/z-1) and tan^{-1}((-1/z)^{1/2})