Range of trig function

i think it should include gamma too,
\begin{align*} &0<\alpha<\beta<\gamma<pi/2 \\ & \implies sin(\alpha)<sin(\beta)\\ & \textup{and also } sin(\alpha)<sin(\gamma)\\\ & \implies sin(\alpha)+sin(\beta)+sin(\gamma)> 3sin(\alpha) \\ & \cos(\alpha)+....<3cos(\alpha)\\ & \implies \frac{\Sigma sin(\alpha)}{\Sigma cos(\alpha)}>tan(\alpha) \\ &= \textup{similarly upper bound.} \end{align*}