Solve $\arccos x\cdot\arcsin x={\pi^2\over 18}$

Question

Can you please help me solve the following trigonometric equation:$$\arccos x\cdot\arcsin x={\pi^2\over 18}$$ This is an very unusual exercise for me so I hope you'll give me some hints on how can I solve the exercise. THank you!

Answer 1

Use the identity $\arccos(x)+\arcsin(x)=\frac{\pi}{2}$ to obtain a quadratic in either $\arcsin(x)$ or $\arccos(x)$.

Though, by inspection, one can say that the answer is $1/2$ or $\sqrt{3}/{2}$.