(1) Let $[x]$ denote the greatest integer not exceeding $x$, then $[\sin 1]+[\cos 2]+[\tan 3]+[\sin 4]+[\cos 5]+[\tan 6]=$ $\qquad$ .
$\begin{array}{l}-4 \text { Hint: Since } 0<1<\frac{\pi}{2}, \frac{\pi}{2}<2<\pi, \frac{3 \pi}{4}<3<\pi, \pi< \\ 4<\frac{3 \pi}{2}, \frac{3 \pi}{2}<5<2 \pi, \frac{7 \pi}{4}<6<2 \pi \text {. Therefore, } \sin 1 \in(0,1), \cos 2 \in \\ (-1,0), \tan 3 \in(-1,0), \sin 4 \in(-1,0), \cos 5 \in(0,1), \\ \tan 6 \in(-1,0) . \Rightarrow[\sin 1]+[\cos 2]+[\tan 3]+[\sin 4]+[\cos 5]+ \\ {[\tan 6]=0+(-1)+(-1)+(-1)+0+(-1)=-4 .}\end{array}$