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We describe a method of integration to obtain identities of the arctangentfunction and show how this method can be applied to the high-accuracycomputation of the constant pi using the equation $\pi = 4 \arctan \left( 1\right)$. Our approach combines the midpoint method with the Taylor expansionseries to enhance accuracy in the subintervals. The accuracy of this method ofintegration is determined by number of subintervals $L$ and by order of theTaylor expansion $M$. This approach provides significant flexibility incomputation since the required convergence in resulting equations can beoptimized through appropriate choices for the integers $L$ and $M$. Samplecomputations are presented to illustrate that even with relatively small valuesof the integers $L$ and $M$ the constant $\pi$ can be computed with highaccuracy.

Identities for the arctangent function by enhanced midpoint integration and the high-accuracy computation of pi