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Here are the key steps. Later on stardard procedure can be applied. Also, refer to this.

\(\tan ^{-1} {1\over {r^4 }} \cr=\tan ^{-1} {2\over {2r^4 }}\cr=\tan^{-1} {2\over {\left( {r^2\sqrt 2}\right)^2}}\cr=\tan^{-1} {2\over {1+\left( {r^2 \sqrt 2}\right)^2-1}}\cr=\tan^{-1} {2\over {1+\left( {r^2\sqrt 2+1}\right)\left( {r^2\sqrt 2-1}\right)}}\cr=\tan^{-1} {{\left( {r^2\sqrt 2+1} \right)-\left( {r^2\sqrt 2-1}\right)}\over {1+\left( {r^2 \sqrt 2+1} \right)\left( {r^2 \sqrt 2-1} \right)}}\)