identity for ${\pi}/4$

Question

I am trying to prove that $${\frac{\pi}{4}}=4{\arctan({\frac{1}{5}})}-{\arctan({\frac{1}{239}})}.$$ I was able to prove $${\frac{\pi}{4}}={\arctan({\frac{1}{2}})}+{\arctan({\frac{1}{3}})}$$ using $$\tan({x+y})={\frac{\tan(x)+\tan(y) }{1-{\tan(x)}{\tan(y)}}}.$$ These identities help us get decimal approximations to $\pi$ using Leibniz's series and $\arctan(1)={\frac{\pi}{4}}$. Not sure how to cope with coefficient $4$. I believe we need to use the formula for $\tan(x-y).$