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Mathematics
Mathematics
Problem
The number of all possible values of
θ
\theta
θ
, where
0
<
θ
<
π
0 < \theta < \pi
0
<
θ
<
π
, for which the system of equations
(
y
+
z
)
cos
3
θ
=
(
x
y
z
)
sin
3
θ
(y+z) \cos 3\theta = (xyz) \sin 3\theta
(
y
+
z
)
cos
3
θ
=
(
x
y
z
)
sin
3
θ
x
sin
3
θ
=
2
cos
3
θ
y
+
2
sin
3
θ
z
x \sin 3\theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z}
x
sin
3
θ
=
y
2
cos
3
θ
+
z
2
sin
3
θ
and
(
x
y
z
)
sin
3
θ
=
(
y
+
2
z
)
cos
3
θ
+
y
sin
3
θ
(xyz) \sin 3\theta = (y+2z) \cos 3\theta + y \sin 3\theta
(
x
y
z
)
sin
3
θ
=
(
y
+
2
z
)
cos
3
θ
+
y
sin
3
θ
have a solution
(
x
0
,
y
0
,
z
0
)
(x_0, y_0, z_0)
(
x
0
,
y
0
,
z
0
)
with
y
0
z
0
≠
0
y_0 z_0 \neq 0
y
0
z
0
=
0
, is .....
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