Prove the following results: (i) $\operatorname{tan}^{-1}(1 / 7)+\tan ^{-1}(1 / 13)=\tan ^{-1}(2 / 9)$ (ii) $\operatorname{sin}^{-1}(12 / 13)+\cos ^{-1}(4 / 5)+\tan ^{-1}(63 / 16)=\pi$