If `tan^(-1)2+tan^(-1)3+theta=pi,` find the value of `thetadot`

Explanation

`tan ^{-1} 2+tan ^{-1} 3+theta=pi `

`Rightarrow tan ^{-1} 2+tan ^{-1} 3=pi-theta `

`Rightarrow pi+tan ^{-1}(frac{2+3}{1-2 times 3})=pi-theta [ a>1, tan ^{-1} a+tan ^{-1} b=pi+tan ^{-1} frac{a+b}{1-a b}] `

`Rightarrow pi+tan ^{-1}(-1)=pi-theta `

`Rightarrow pi-frac{pi}{4}=pi-theta `

Thus, `theta=frac{pi}{4}`