Solve $\int_{0}^{\pi/2} \arccos\left( \frac{\cos(x)}{1+2\cos(x)} \right) \mathrm dx$ [closed]

calculus definite-integrals integration

Here is the method to evaluate this integral. enter image description here

enter image description here

enter image description here

enter image description here

enter image description here

Source:- Some very challenging calculus problems by Joseph Breen

Related

understanding the commutator of dihedral group [duplicate]
How many continuous function $f(x)$ exist such that $\int_{0}^{1}f(x)\big(1-f(x)\big)\mathrm dx = \frac{1}{4}$? [closed]
Norm of a fractional ideal of an order of an algebraic number field
Theorem $2$ (Variational principle for the principal eigenvalue)
Automorphisms of a Cyclic Group
simple tools to extract Re,Im,Abs... of any complex function
$A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category
Why is there no solution with radicals for the quintic equation $x^5-x+1=0$? [closed]
Why does $\sin(45)=\frac{\sqrt2}{2}$ when $45^{\circ}= \frac{\pi}{4}$ radians?
Laurent Series of operator-value function
Prove that $1/f$ is Riemann integrable on $[a,b]$
Need help regarding a proof in First Order Logic