BELG * Find the value of the algebraic expression
$$
\arcsin \frac{1}{\sqrt{10}}+\arccos \frac{7}{\sqrt{50}}+\arctan \frac{7}{31}+\operatorname{arccot} 10
$$
By using the geometric meaning of complex number multiplication, we know that the value of (1) is equal to the argument of the following complex number
$$
z=(3+\mathrm{i})(7+\mathrm{i})(31+7 \mathrm{i})(10+\mathrm{i})
$$

Since each angle in (1) is acute, the value we are looking for is the principal argument of $z$. Notice that
$$
\begin{aligned}
z & =(20+10 \mathrm{i})(303+101 \mathrm{i})=1010(2+\mathrm{i})(3+\mathrm{i}) \\
& =1010(5+5 \mathrm{i})=5050(1+\mathrm{i}),
\end{aligned}
$$

Therefore, $\arg z=\frac{\pi}{4}$. Hence, the value of the given algebraic expression is $\frac{\pi}{4}$.