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  $$ \begin{gathered} \cos \frac{\pi}{15} \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{7 \pi}{15}=-\cos \frac{\pi}{15} \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15}=\frac{1}{16} \\ \cos \frac{3 \pi}{15} \cos \frac{6 \pi}{15}=\frac{1}{4}, \quad \cos \frac{5 \pi}{15}=\frac{1}{2} . \end{gathered} $$  Multiplying these equalities, we get that the required product $P$ equals 1/128.