\[t'=\frac{t-\frac{vt}{c}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=t\cdot \frac{1-\frac{v}{c}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=t\cdot \frac{1-cos\alpha }{sin\alpha }=t\cdot tg\frac{\alpha }{2}=t\cdot \sqrt{\frac{c-v}{c+v}}\]