21. (HUN 2) Without using any tables, find the exact value of the product
$$
P=\cos \frac{\pi}{15} \cos \frac{2 \pi}{15} \cos \frac{3 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{5 \pi}{15} \cos \frac{6 \pi}{15} \cos \frac{7 \pi}{15} .
$$
21. Using the formula
$$
\cos x \cos 2 x \cos 4 x \cdots \cos 2^{n-1} x=\frac{\sin 2^{n} x}{2^{n} \sin x},
$$
which is shown by simple induction, we obtain
$$
\begin{array}{c}
\cos \frac{\pi}{15} \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{7 \pi}{15}=-\cos \frac{\pi}{15} \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15}=\frac{1}{16}, \\
\cos \frac{3 \pi}{15} \cos \frac{6 \pi}{15}=\frac{1}{4}, \quad \cos \frac{5 \pi}{15}=\frac{1}{2} .
\end{array}
$$

Multiplying these equalities, we get that the required product $P$ equals $1 / 128$