The value of cos15⁰-cos 75⁰+cos 135⁰

$$\begin{gathered} \cos {15}^0-\cos {75}^0+\cos {135}^0 \\ \cos {15}^0+\cos {135}^0-\cos {75}^0 \\ =2\cos \left(\frac{{150}^0}{2}\right)\cos \left(\frac{{120}^0}{2}\right)-\cos {75}^0 \\ =\cos {75}^0-\cos {60}^0-\cos {75}^0 \\ =2 \cos {75}^0\frac{1}{2}-\cos {75}^0 \\ =\cos {75}^0-\cos {75}^0 \\ =0 \end{gathered}$$