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Problem
Problem
Statement I
For any
△
A
B
C
\triangle ABC
△
A
B
C
sin
(
A
+
B
+
C
3
)
≥
sin
A
+
sin
B
+
sin
C
3
\sin\left(\frac{A+B+C}{3}\right) \ge \frac{\sin A + \sin B + \sin C}{3}
sin
(
3
A
+
B
+
C
)
≥
3
sin
A
+
sin
B
+
sin
C
Statement II
y
=
sin
x
y = \sin x
y
=
sin
x
is concave downward for
x
∈
(
0
,
π
]
x \in (0, \pi]
x
∈
(
0
,
π
]
.
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