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Problem
Problem
Suppose
x
1
=
tan
−
1
2
>
x
2
>
x
3
>
…
x_1 = \tan^{-1} 2 > x_2 > x_3 > \dots
x
1
=
tan
−
1
2
>
x
2
>
x
3
>
…
are the real numbers satisfying
sin
(
x
n
+
1
−
x
n
)
+
2
−
(
n
+
1
)
⋅
sin
x
n
⋅
sin
x
n
+
1
=
0
\sin(x_{n+1} - x_n) + 2^{-(n+1)} \cdot \sin x_n \cdot \sin x_{n+1} = 0
sin
(
x
n
+
1
−
x
n
)
+
2
−
(
n
+
1
)
⋅
sin
x
n
⋅
sin
x
n
+
1
=
0
for all
n
>
1
n > 1
n
>
1
and
l
=
lim
n
→
∞
x
n
l = \lim_{n \to \infty} x_n
l
=
lim
n
→
∞
x
n
, the value of
[
4
l
]
[4l]
[
4
l
]
is ..... (where
[
⋅
]
[\cdot]
[
⋅
]
denotes greatest integer function).
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