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Mathematics
Mathematics
Problem
If the range of
f
(
θ
)
=
sin
4
θ
+
3
cos
2
θ
sin
4
θ
+
cos
2
θ
f(\theta) = \frac{\sin^4 \theta + 3 \cos^2 \theta}{\sin^4 \theta + \cos^2 \theta}
f
(
θ
)
=
s
i
n
4
θ
+
c
o
s
2
θ
s
i
n
4
θ
+
3
c
o
s
2
θ
,
θ
∈
R
\theta \in \mathbb{R}
θ
∈
R
is
[
α
,
β
]
[\alpha, \beta]
[
α
,
β
]
, then the sum of the infinite G.P., whose first term is 64 and the common ratio is
α
β
\frac{\alpha}{\beta}
β
α
, is equal to ________.
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