$\cos \theta =2{{\cos }^{2}}\frac{\theta }{2}-1\Rightarrow \frac{1}{5}=2{{\cos }^{2}}\frac{\theta }{2}-1\Rightarrow 2{{\cos }^{2}}\frac{\theta }{2}=\frac{1}{5}+1\Rightarrow 2{{\cos }^{2}}\frac{\theta }{2}=\frac{6}{5}\Rightarrow {{\cos }^{2}}\frac{\theta }{2}=\frac{3}{5}$ $\Rightarrow {{\sin }^{2}}\frac{\theta }{2}=1-{{\cos }^{2}}\frac{\theta }{2}=1-\frac{3}{5}=\frac{2}{5}$ و بنابراین: $2{{\sin }^{2}}\frac{\theta }{2}-{{\cos }^{2}}\frac{\theta }{2}=2(\frac{2}{5})-\frac{3}{5}=\frac{1}{5}$