The number of solutions the equation cos($\mathrm{\theta }$).cos(π$\mathrm{\theta }$) = 1 has_____

$\begin{array}{l}\cos \left(\mathrm{\theta }\right)=1\text{ and }\cos \left(\mathrm{\pi \theta }\right)=1\dots .\text{ (i) }\\ \text{ or }\cos \left(\mathrm{\theta }\right)=-1\text{ and }\cos \left(\mathrm{\pi \theta }\right)=-1\end{array}$
Equation (ii) is not possible for any $\mathrm{\theta }$ . Therefore
$\mathrm{\theta }$ = 0 is the only solution. since $\mathrm{\theta }$ is irrational as
well as odd integer (not possible)