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Problem
Problem
If equation
x
2
tan
2
θ
−
(
2
tan
θ
)
x
+
1
=
0
x^2 \tan^2 \theta - (2 \tan \theta)x + 1 = 0
x
2
tan
2
θ
−
(
2
tan
θ
)
x
+
1
=
0
and
(
1
1
+
log
b
a
c
)
x
2
+
(
1
1
+
log
c
a
b
)
x
+
(
1
1
+
log
a
b
c
−
1
)
=
0
\left( \frac{1}{1 + \log_b ac} \right) x^2 + \left( \frac{1}{1 + \log_c ab} \right) x + \left( \frac{1}{1 + \log_a bc} - 1 \right) = 0
(
1
+
lo
g
b
a
c
1
)
x
2
+
(
1
+
lo
g
c
ab
1
)
x
+
(
1
+
lo
g
a
b
c
1
−
1
)
=
0
(where
a
,
b
,
c
>
1
a, b, c > 1
a
,
b
,
c
>
1
) have a common root and then 2nd equation has equal roots, then number of possible value of
θ
\theta
θ
in
(
0
,
π
)
(0, \pi)
(
0
,
π
)
is
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